Veda Skills Logical Reasoning Unit 17: Mirror, Water Images and Paper Folding
- 3 topics
- 150 MCQs
- 10 short answers
- 3 long answers
- 37 flashcards
- 3 games
- ~115 min read
- English
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Mirror and Water Images
Find the mirror image and the water image of letters, numbers, words, clocks and figures, and spot the traps examiners set: the water image offered as a mirror image, letters reversed but not flipped, and half-flipped figures.
What you will be able to do
- I can draw the mirror image of a word or number in the correct order with each letter flipped.
- I can tell a mirror image from a water image at a glance.
- I can find the time shown by the mirror image of a clock.
- I can pick the true image of a figure by checking one asymmetric part.
Key points
A vertical mirror (placed to the left or right) swaps left and right; top and bottom stay as they are.
A water image (mirror below or above) swaps top and bottom; left and right stay as they are.
In the mirror image of a word, the letters come in reverse order and each letter is flipped sideways.
In the water image of a word, the order stays the same and each letter turns upside down.
A, H, I, M, O, T, U, V, W, X, Y look the same in a mirror; B, C, D, E, H, I, K, O, X look the same in water.
Mirror time of a clock = 11:60 − actual time (use 23:60 for a 24-hour clock); the rule also works backwards.
The water image of a clock flips each hand about the 3–9 line, so the minute hand at M moves to 30 − M.
To choose between figures, follow one small asymmetric part (a dot, a flag, a filled corner) rather than the whole figure.
Full explanation
Priya and the ambulance
Priya is waiting at a red light in Pune. An ambulance stops behind her father's car. On its bonnet she sees strange letters: ƎƆИA⅃UᗺMA. Then she looks in the side mirror and reads AMBULANCE clearly!
The painters wrote the mirror image of the word on purpose. Today you will learn to make and read such images in seconds.
Two kinds of image
- Mirror image (mirror on the left or right, line MN standing up): left and right swap, top and bottom stay.
- Water image (water or mirror below, line MN lying flat): top and bottom swap, left and right stay.
A word in a mirror is read backwards with every letter turned sideways; a word in water keeps its order but every letter stands on its head.
Letters that do not change
A letter with a vertical line of symmetry looks the same in a mirror: A, H, I, M, O, T, U, V, W, X, Y.
A letter with a horizontal line of symmetry looks the same in water: B, C, D, E, H, I, K, O, X.
Shortcut: a word looks the same in a mirror only if it is a palindrome made of mirror letters (MOM, TOOT, WOW). A word looks the same in water if every letter is a water letter (BOX, CODE, HIDE).
Worked example: a word in a mirror
Find the mirror image of BANK with the mirror on the right.
- Reverse the order: K, N, A, B.
- Flip each letter sideways: K and N and B change, A does not.
The image reads ꓘИAᗺ. Trap options: KNAB (order reversed, letters not flipped), ᗺAИꓘ (letters flipped, order kept) and the upside-down water image.
Clocks in a mirror
The mirror image of a clock shows a different time. Real time and mirror time always add up to 12:00, so
$$\text{mirror time} = 11{:}60 - \text{real time}$$
Example: real time 3:40 gives $11{:}60 - 3{:}40 = 8{:}20$. The rule works both ways: if the mirror shows 8:20, the real time is 3:40.
Figures: follow one part
For a figure, do not try to flip everything in your head. Pick one asymmetric part, such as a filled triangle in a corner or a flag, and ask where it must go.
- Mirror: a part on the top-left moves to the top-right.
- Water: a part on the top-left moves to the bottom-left.
- Rotation by 180°: top-left goes to bottom-right. This is neither image, and examiners love to offer it.
Exam shortcuts
- Mirror image of a word: reverse the order, flip each letter sideways.
- Water image: same order, each letter upside down.
- Symmetric letters cannot help you; look for B, C, D, E, F, G, J, K, L, N, P, Q, R, S, Z.
- Mirror clock: 11:60 − time.
- A mirror image and a water image of the same object differ by a 180° turn.
Back to Priya
At home Priya writes her name PRIYA on a card in mirror writing: AYIЯꟼ. Her brother holds it up to the bathroom mirror and reads PRIYA. "Now I know why the ambulance looked odd," she says. "It was written for mirrors, not for people."
Mind map
The whole topic on one page.
Concepts and terms
A plane mirror swaps left and right. Raise your right hand in front of a mirror and the image raises its left.
The image in still water below an object: the top goes to the bottom and the bottom to the top, with left and right unchanged.
A letter with a vertical line of symmetry (like A) is unchanged in a mirror; one with a horizontal line (like B) is unchanged in water.
Mirror and real times add up to 12:00, so mirror time = 11:60 − real time.
Did you know
AMBULANCE is painted in mirror writing on the front of ambulances so that drivers ahead can read it in their rear-view mirrors.
Leonardo da Vinci wrote many of his notebooks in mirror writing, from right to left.
Memory tricks
Mirror vs water — Mirror: sides swap. Water: heads swap. — In a mirror the left and right sides change places; in water the head goes to the feet.
Mirror time — Eleven-sixty minus — Subtract the time from 11:60 to read a mirror clock.
Practice MCQs with answers (61)
- A 1
- B 2
- C 3
- D 4
Show answer
Why:
In a mirror image, the order of the characters reverses and each one flips sideways; top and bottom do not change. Only figure (1) does both. The other figures show a different image or only half of the change.
- A 1
- B 2
- C 3
- D 4
Show answer
Why:
In a mirror image, the order of the characters reverses and each one flips sideways; top and bottom do not change. Only figure (2) does both. The other figures show a different image or only half of the change.
- A 1
- B 2
- C 3
- D 4
Show answer
Why:
In a mirror image, the order of the characters reverses and each one flips sideways; top and bottom do not change. Only figure (3) does both. The other figures show a different image or only half of the change.
- A 1
- B 2
- C 3
- D 4
Show answer
Why:
In a mirror image, the order of the characters reverses and each one flips sideways; top and bottom do not change. Only figure (4) does both. The other figures show a different image or only half of the change.
- A 1
- B 2
- C 3
- D 4
Show answer
Why:
In a mirror image, the order of the characters reverses and each one flips sideways; top and bottom do not change. Only figure (1) does both. The other figures show a different image or only half of the change.
- A 1
- B 2
- C 3
- D 4
Show answer
Why:
In a mirror image, the order of the characters reverses and each one flips sideways; top and bottom do not change. Only figure (2) does both. The other figures show a different image or only half of the change.
- A 1
- B 2
- C 3
- D 4
Show answer
Why:
In a mirror image, the order of the characters reverses and each one flips sideways; top and bottom do not change. Only figure (3) does both. The other figures show a different image or only half of the change.
- A 1
- B 2
- C 3
- D 4
Show answer
Why:
In a mirror image, the order of the characters reverses and each one flips sideways; top and bottom do not change. Only figure (4) does both. The other figures show a different image or only half of the change.
- A 1
- B 2
- C 3
- D 4
Show answer
Why:
In a mirror image, the order of the characters reverses and each one flips sideways; top and bottom do not change. Only figure (1) does both. The other figures show a different image or only half of the change.
- A 1
- B 2
- C 3
- D 4
Show answer
Why:
In a mirror image, the order of the characters reverses and each one flips sideways; top and bottom do not change. Only figure (2) does both. The other figures show a different image or only half of the change.
- A 1
- B 2
- C 3
- D 4
Show answer
Why:
In a water image, the order stays the same and each character turns upside down; left and right do not change. Only figure (3) does both. The other figures show a different image or only half of the change.
- A 1
- B 2
- C 3
- D 4
Show answer
Why:
In a water image, the order stays the same and each character turns upside down; left and right do not change. Only figure (4) does both. The other figures show a different image or only half of the change.
- A 1
- B 2
- C 3
- D 4
Show answer
Why:
In a water image, the order stays the same and each character turns upside down; left and right do not change. Only figure (1) does both. The other figures show a different image or only half of the change.
- A 1
- B 2
- C 3
- D 4
Show answer
Why:
In a water image, the order stays the same and each character turns upside down; left and right do not change. Only figure (2) does both. The other figures show a different image or only half of the change.
- A 1
- B 2
- C 3
- D 4
Show answer
Why:
In a water image, the order stays the same and each character turns upside down; left and right do not change. Only figure (3) does both. The other figures show a different image or only half of the change.
- A 1
- B 2
- C 3
- D 4
Show answer
Why:
In a water image, the order stays the same and each character turns upside down; left and right do not change. Only figure (4) does both. The other figures show a different image or only half of the change.
- A 1
- B 2
- C 3
- D 4
Show answer
Why:
In a water image, the order stays the same and each character turns upside down; left and right do not change. Only figure (1) does both. The other figures show a different image or only half of the change.
- A 1
- B 2
- C 3
- D 4
Show answer
Why:
In a water image, the order stays the same and each character turns upside down; left and right do not change. Only figure (2) does both. The other figures show a different image or only half of the change.
- A DAD
- B MAT
- C NUN
- D MOM
Show answer
Why:
MOM reads the same backwards and uses only mirror-safe letters. DAD: D flips. MAT: not the same backwards. NUN: N flips.
- A TOOT
- B NOON
- C TOTE
- D POOP
Show answer
Why:
TOOT reads the same backwards and uses only mirror-safe letters. NOON: N flips. TOTE: not the same backwards. POOP: P flips.
- A WOK
- B WOW
- C SOS
- D BOB
Show answer
Why:
WOW reads the same backwards and uses only mirror-safe letters. BOB: B flips. WOK: not the same backwards. SOS: S flips.
- A ANNA
- B OTTER
- C OTTO
- D EYE
Show answer
Why:
OTTO reads the same backwards and uses only mirror-safe letters. ANNA: N flips. OTTER: not the same backwards. EYE: E flips.
- A FOX
- B BOY
- C BUS
- D BOX
Show answer
Why:
Every letter of BOX has a horizontal line of symmetry. BUS: U turns over. FOX: F turns over. BOY: Y turns over.
- A CODE
- B COPE
- C CORE
- D COKES
Show answer
Why:
Every letter of CODE has a horizontal line of symmetry. COPE: P turns over. CORE: R turns over. COKES: S turns over.
- A HIGH
- B HIDE
- C RIDE
- D HIRE
Show answer
Why:
Every letter of HIDE has a horizontal line of symmetry. HIRE: R turns over. HIGH: G turns over. RIDE: R turns over.
- A DESK
- B NECK
- C DECK
- D DUCK
Show answer
Why:
Every letter of DECK has a horizontal line of symmetry. DESK: S turns over. NECK: N turns over. DUCK: U turns over.
- A 6
- B 4
- C 2
- D 3
Show answer
Why:
They are A, H, I: 3 letters with a vertical line of symmetry.
- A 3
- B 2
- C 4
- D 5
Show answer
Why:
They are M, O, T: 3 letters with a vertical line of symmetry.
- A 3
- B 6
- C 7
- D 5
Show answer
Why:
They are B, C, D, E, H, I: 6 letters with a horizontal line of symmetry.
- A 2
- B 0
- C 1
- D 6
Show answer
Why:
They are X: 1 letters with a horizontal line of symmetry.
- A 1
- B 6
- C 4
- D 5
Show answer
Why:
They are U, V, W, X, Y: 5 letters with a vertical line of symmetry.
- A 8:20
- B 3:40
- C 2:50
- D 9:20
Show answer
Why:
Real time and mirror time add up to 12:00: 11:60 − 3:40 = 8:20.
- A 4:45
- B 3:45
- C 8:15
- D 10:15
Show answer
Why:
Real time and mirror time add up to 12:00: 11:60 − 8:15 = 3:45.
- A 10:25
- B 8:05
- C 1:35
- D 2:35
Show answer
Why:
Real time and mirror time add up to 12:00: 11:60 − 10:25 = 1:35.
- A 4:40
- B 11:10
- C 1:50
- D 10:10
Show answer
Why:
Real time and mirror time add up to 12:00: 11:60 − 1:50 = 10:10.
- A 7:35
- B 2:05
- C 8:35
- D 4:25
Show answer
Why:
Real time and mirror time add up to 12:00: 11:60 − 4:25 = 7:35.
- A 9:25
- B 2:55
- C 3:55
- D 9:05
Show answer
Why:
Real time and mirror time add up to 12:00: 11:60 − 9:05 = 2:55.
- A 5:55
- B 12:25
- C 11:25
- D 12:35
Show answer
Why:
Real time and mirror time add up to 12:00: 11:60 − 12:35 = 11:25.
- A 6:50
- B 6:10
- C 12:20
- D 5:50
Show answer
Why:
Real time and mirror time add up to 12:00: 11:60 − 6:10 = 5:50.
- A 1
- B 2
- C 3
- D 4
Show answer
Why:
In the mirror image each hand moves to the same angle on the other side of the 12–6 line. Figure (3) has both hands placed this way and reads 9:50 (11:60 − 2:10).
- A 1
- B 2
- C 3
- D 4
Show answer
Why:
In the mirror image each hand moves to the same angle on the other side of the 12–6 line. Figure (4) has both hands placed this way and reads 4:40 (11:60 − 7:20).
- A 1
- B 2
- C 3
- D 4
Show answer
Why:
In the water image each hand moves to the same angle on the other side of the 3–9 line. Figure (1) has both hands placed this way.
- A 1
- B 2
- C 3
- D 4
Show answer
Why:
In the mirror image each hand moves to the same angle on the other side of the 12–6 line. Figure (2) has both hands placed this way and reads 1:25 (11:60 − 10:35).
- A 1
- B 2
- C 3
- D 4
Show answer
Why:
In the water image each hand moves to the same angle on the other side of the 3–9 line. Figure (3) has both hands placed this way.
- A 1
- B 2
- C 3
- D 4
Show answer
Why:
Follow one part: in a mirror image every part keeps its height but moves to the other side, and is itself flipped. Only figure (4) does this; the others are flipped top to bottom, turned through 180°, turned a quarter clockwise.
- A 1
- B 2
- C 3
- D 4
Show answer
Why:
Follow one part: in a mirror image every part keeps its height but moves to the other side, and is itself flipped. Only figure (1) does this; the others are flipped top to bottom, turned through 180°, turned a quarter clockwise.
- A 1
- B 2
- C 3
- D 4
Show answer
Why:
Follow one part: in a water image every part keeps its side but moves from top to bottom, and is itself flipped. Only figure (2) does this; the others are flipped left to right, turned through 180°, turned a quarter clockwise.
- A 1
- B 2
- C 3
- D 4
Show answer
Why:
Follow one part: in a mirror image every part keeps its height but moves to the other side, and is itself flipped. Only figure (3) does this; the others are flipped top to bottom, turned through 180°, turned a quarter clockwise.
- A 1
- B 2
- C 3
- D 4
Show answer
Why:
Follow one part: in a water image every part keeps its side but moves from top to bottom, and is itself flipped. Only figure (4) does this; the others are flipped left to right, turned through 180°, turned a quarter clockwise.
- A 1
- B 2
- C 3
- D 4
Show answer
Why:
Follow one part: in a mirror image every part keeps its height but moves to the other side, and is itself flipped. Only figure (1) does this; the others are flipped top to bottom, turned through 180°, turned a quarter clockwise.
- A 1
- B 2
- C 3
- D 4
Show answer
Why:
Follow one part: in a water image every part keeps its side but moves from top to bottom, and is itself flipped. Only figure (2) does this; the others are flipped left to right, turned through 180°, turned a quarter clockwise.
- A 1
- B 2
- C 3
- D 4
Show answer
Why:
Follow one part: in a mirror image every part keeps its height but moves to the other side, and is itself flipped. Only figure (3) does this; the others are flipped top to bottom, turned through 180°, turned a quarter clockwise.
- A Its left hand
- B Both hands
- C Neither hand
- D Its right hand
Show answer
Why:
A plane mirror swaps left and right (lateral inversion).
- A E
- B X
- C A
- D B
Show answer
Why:
X has both a vertical and a horizontal line of symmetry. A is mirror-safe only; B and E are water-safe only.
- A It starts and ends with a vowel
- B It uses only letters like B, C, D, E
- C It reads the same backwards and uses only letters like A, H, M, O, T
- D It has an even number of letters
Show answer
Why:
The mirror reverses the order and flips each letter, so both the order and every letter must survive the flip.
- A a shift to the right
- B a rotation of 90°
- C nothing; they are the same
- D a rotation of 180°
Show answer
Why:
Mirror flips x, water flips y; flipping both is the same as turning through 180°.
- A 2
- B 1
- C 3
- D 4
Show answer
Why:
Only 0 and 8 have a vertical line of symmetry, so the answer is 2.
- A Both A and R are true, and R is the correct explanation of A
- B Both A and R are true, but R is not the correct explanation of A
- C A is true but R is false
- D A is false but R is true
Show answer
Why:
11:60 − 2:30 = 9:30, and 2:30 + 9:30 = 12:00. R is the rule behind A.
- A Both A and R are true, and R is the correct explanation of A
- B Both A and R are true, but R is not the correct explanation of A
- C A is true but R is false
- D A is false but R is true
Show answer
Why:
R is true, so HIDE looks the same in water, not in a mirror: a mirror would reverse it to EDIH and flip D and E. A is false.
- A 1 only
- B 2 only
- C Both 1 and 2
- D Neither 1 nor 2
Show answer
Why:
Water swaps top and bottom only, so 1 is false; a mirror reverses the order, so 2 is true.
- A 1 only
- B 2 only
- C Both 1 and 2
- D Neither 1 nor 2
Show answer
Why:
11:60 − 6:00 = 6:00, and 11:60 − 12:30 gives −0:30 + 12:00 = 11:30. Both are true.
Important short questions (4)
Write the letters in reverse order, then flip every letter left to right. Letters such as A, H, M, O, T stay the same.
11:60 − 5:35 = 6:25.
H, I, O and X, because each has both a vertical and a horizontal line of symmetry.
Follow one part that is near the top. In the mirror image it stays near the top but moves to the other side; in the water image it moves to the bottom on the same side.
Long answer questions (1)
Mirror (line on the right): the order reverses to B, A, C and each letter flips sideways; A is unchanged, B and C face left.
Water (line below): the order stays C, A, B and each letter turns upside down; C and B look the same, A stands on its point.
Rotation by 180° does both flips at once: order B, A, C with every letter upside down and reversed. It is the mirror image of the water image, not an image of CAB itself.
Flashcards (13)
Play this topic
- Image or not?
Paper Folding and Cutting
Predict how a folded and punched or cut sheet looks when opened, count the holes from the number of folds, and fold a transparent sheet with a design in your head.
What you will be able to do
- I can open a folded sheet step by step, last fold first.
- I can count holes after opening from the number of folds and punches.
- I can tell a reflected copy from a shifted copy of a hole or cut.
- I can fold a transparent sheet with a design and predict the result.
Key points
Every fold doubles the number of layers: 1 fold gives 2 layers, 2 folds 4, 3 folds 8.
A hole punched through all layers appears once in every layer, so holes after opening = punches × 2^folds (when no hole is on a fold).
Open the folds in reverse order: undo the last fold first.
Each opening adds a mirror image of every hole across that fold line.
Holes are reflected, not shifted: a triangle pointing right becomes one pointing left on the other side of a vertical fold.
A cut touching a fold line joins its reflection, so a triangular notch on a fold opens into a diamond.
In transparent-sheet folding, the half that moves lands on the other half as its mirror image; the half that stays is unchanged.
Full explanation
Meena's rangoli stencil
Meena wants a stencil for the Diwali rangoli at her school in Jaipur. Her teacher shows a trick: fold a square sheet twice, punch two holes, and open it. Four copies of each hole appear, perfectly placed!
Meena's friend guesses where the holes will be before opening, and gets it wrong. This topic shows how to get it right every time.
Folds make layers
Each time you fold a sheet in half, the number of layers doubles. A punch goes through every layer, so it makes one hole in each.
$$\text{holes} = \text{punches} \times 2^{\text{folds}}$$
This holds when no hole sits on a fold line.
Opening: last fold first
The last fold is on top, so open it first. Each time you open a fold, imagine the fold line is a mirror: every hole gets a mirror copy on the other side, at the same distance from the line.
Reflect, do not shift
The commonest wrong option shows the holes in the right places but not flipped. A round hole looks the same either way, so examiners use triangles, arrows and half-circles.
Check: a triangle whose right angle is near the fold must have its copy's right angle near the fold too.
Diagonal folds
A fold along a diagonal works the same way, with the diagonal as the mirror. A hole near the top edge of the folded triangle reappears near the side edge after opening.
Cuts on a fold
If a cut touches a fold line, it joins its own reflection. A small triangle cut at a folded edge opens into a diamond; a half-circle cut on a fold opens into a full circle.
Transparent sheets
Some questions give a transparent sheet with a design and ask how it looks after one fold. The moving half lands on the other half as its mirror image across the fold, and the other half stays as it is.
Exam shortcuts
- Count first: punches × $2^{\text{folds}}$ removes wrong options fast.
- Open the last fold first.
- Every copy is a reflection: check one asymmetric hole.
- A notch on a fold doubles into one bigger cut.
- Transparent fold: moving half flips, staying half does not.
Back to Meena
Meena folds her sheet left over right, then top over bottom, and punches a circle and a triangle. Before opening she says: "Four layers, so four circles and four triangles, each flipped at the folds." She opens it, and she is right. The rangoli stencil is ready.
Mind map
The whole topic on one page.
Concepts and terms
Folding in half puts one part on top of another, so the number of layers doubles with each fold.
Opening a fold places a mirror copy of everything across the fold line, as if the fold line were a mirror.
The last fold made is on top, so it is the first to be opened.
On a transparent sheet both designs stay visible after folding: one as it was, the other as its mirror image.
Did you know
Sanjhi, the paper-cutting art of Mathura, makes symmetric designs by cutting a folded sheet.
A sheet of paper cannot usually be folded in half more than 7 or 8 times, because 8 folds already make 256 layers.
Memory tricks
Unfolding — Last in, first out — Open the last fold first, like taking plates off a pile.
Hole count — Double per fold — Punches × 2 × 2 × … once for each fold.
Practice MCQs with answers (44)
- A 1
- B 2
- C 3
- D 4
Show answer
Why:
Unfold one step at a time, last fold first. Each unfolding adds a mirror copy of every hole across that fold line, so 2 becomes 4. Figure (2) has all of them, each reflected (not just shifted).
- A 1
- B 2
- C 3
- D 4
Show answer
Why:
Unfold one step at a time, last fold first. Each unfolding adds a mirror copy of every hole across that fold line, so 2 becomes 4. Figure (3) has all of them, each reflected (not just shifted).
- A 1
- B 2
- C 3
- D 4
Show answer
Why:
Unfold one step at a time, last fold first. Each unfolding adds a mirror copy of every hole across that fold line, so 2 becomes 4. Figure (4) has all of them, each reflected (not just shifted).
- A 1
- B 2
- C 3
- D 4
Show answer
Why:
Unfold one step at a time, last fold first. Each unfolding adds a mirror copy of every hole across that fold line, so 2 becomes 4. Figure (1) has all of them, each reflected (not just shifted).
- A 1
- B 2
- C 3
- D 4
Show answer
Why:
Unfold one step at a time, last fold first. Each unfolding adds a mirror copy of every hole across that fold line, so 2 becomes 4. Figure (2) has all of them, each reflected (not just shifted).
- A 1
- B 2
- C 3
- D 4
Show answer
Why:
Unfold one step at a time, last fold first. Each unfolding adds a mirror copy of every hole across that fold line, so 1 becomes 4. Figure (3) has all of them, each reflected (not just shifted).
- A 1
- B 2
- C 3
- D 4
Show answer
Why:
Unfold one step at a time, last fold first. Each unfolding adds a mirror copy of every hole across that fold line, so 2 becomes 8. Figure (4) has all of them, each reflected (not just shifted).
- A 1
- B 2
- C 3
- D 4
Show answer
Why:
Unfold one step at a time, last fold first. Each unfolding adds a mirror copy of every hole across that fold line, so 2 becomes 8. Figure (1) has all of them, each reflected (not just shifted).
- A 1
- B 2
- C 3
- D 4
Show answer
Why:
Unfold one step at a time, last fold first. Each unfolding adds a mirror copy of every hole across that fold line, so 2 becomes 8. Figure (2) has all of them, each reflected (not just shifted).
- A 1
- B 2
- C 3
- D 4
Show answer
Why:
Unfold one step at a time, last fold first. Each unfolding adds a mirror copy of every hole across that fold line, so 1 becomes 4. Figure (3) has all of them, each reflected (not just shifted).
- A 1
- B 2
- C 3
- D 4
Show answer
Why:
Unfold one step at a time, last fold first. Each unfolding adds a mirror copy of every hole across that fold line, so 2 becomes 8. Figure (4) has all of them, each reflected (not just shifted).
- A 1
- B 2
- C 3
- D 4
Show answer
Why:
Unfold one step at a time, last fold first. Each unfolding adds a mirror copy of every hole across that fold line, so 2 becomes 8. Figure (1) has all of them, each reflected (not just shifted).
- A 1
- B 2
- C 3
- D 4
Show answer
Why:
Unfold one step at a time, last fold first. Each unfolding adds a mirror copy of every hole across that fold line, so 1 becomes 8. Figure (2) has all of them, each reflected (not just shifted).
- A 1
- B 2
- C 3
- D 4
Show answer
Why:
Unfold one step at a time, last fold first. Each unfolding adds a mirror copy of every hole across that fold line, so 2 becomes 4. Figure (3) has all of them, each reflected (not just shifted).
- A 1
- B 2
- C 3
- D 4
Show answer
Why:
Unfold one step at a time, last fold first. Each unfolding adds a mirror copy of every hole across that fold line, so 2 becomes 8. Figure (4) has all of them, each reflected (not just shifted).
- A 1
- B 2
- C 3
- D 4
Show answer
Why:
Unfold one step at a time, last fold first. Each unfolding adds a mirror copy of every hole across that fold line, so 2 becomes 4. Figure (1) has all of them, each reflected (not just shifted).
- A 1
- B 2
- C 3
- D 4
Show answer
Why:
Unfold one step at a time, last fold first. Each unfolding adds a mirror copy of every cut across that fold line, so 1 becomes 2. Figure (2) has all of them, each reflected (not just shifted).
- A 1
- B 2
- C 3
- D 4
Show answer
Why:
Unfold one step at a time, last fold first. Each unfolding adds a mirror copy of every cut across that fold line, so 1 becomes 4. Figure (3) has all of them, each reflected (not just shifted).
- A 1
- B 2
- C 3
- D 4
Show answer
Why:
Unfold one step at a time, last fold first. Each unfolding adds a mirror copy of every cut across that fold line, so 2 becomes 4. Figure (4) has all of them, each reflected (not just shifted).
- A 1
- B 2
- C 3
- D 4
Show answer
Why:
Unfold one step at a time, last fold first. Each unfolding adds a mirror copy of every cut across that fold line, so 2 becomes 8. Figure (1) has all of them, each reflected (not just shifted).
- A 1
- B 2
- C 3
- D 4
Show answer
Why:
The half that moves lands on the other half as its mirror image across the fold line, and the half that stays does not change. Figure (2) shows this.
- A 1
- B 2
- C 3
- D 4
Show answer
Why:
The half that moves lands on the other half as its mirror image across the fold line, and the half that stays does not change. Figure (3) shows this.
- A 1
- B 2
- C 3
- D 4
Show answer
Why:
The half that moves lands on the other half as its mirror image across the fold line, and the half that stays does not change. Figure (4) shows this.
- A 1
- B 2
- C 3
- D 4
Show answer
Why:
The half that moves lands on the other half as its mirror image across the fold line, and the half that stays does not change. Figure (1) shows this.
- A 1
- B 2
- C 3
- D 4
Show answer
Why:
The half that moves lands on the other half as its mirror image across the fold line, and the half that stays does not change. Figure (2) shows this.
- A 1
- B 2
- C 3
- D 4
Show answer
Why:
The half that moves lands on the other half as its mirror image across the fold line, and the half that stays does not change. Figure (3) shows this.
- A 5
- B 6
- C 3
- D 12
Show answer
Why:
1 fold make 2 layers, and each hole goes through every layer: 3 × 2 = 6.
- A 16
- B 6
- C 8
- D 4
Show answer
Why:
2 folds make 4 layers, and each hole goes through every layer: 2 × 4 = 8.
- A 4
- B 16
- C 6
- D 8
Show answer
Why:
3 folds make 8 layers, and each hole goes through every layer: 1 × 8 = 8.
- A 24
- B 18
- C 12
- D 48
Show answer
Why:
3 folds make 8 layers, and each hole goes through every layer: 3 × 8 = 24.
- A 4
- B 8
- C 16
- D 6
Show answer
Why:
1 fold make 2 layers, and each hole goes through every layer: 4 × 2 = 8.
- A 4
- B 16
- C 8
- D 6
Show answer
Why:
2 folds make 4 layers, and each hole goes through every layer: 2 × 4 = 8.
- A 17
- B 8
- C 32
- D 16
Show answer
Why:
4 folds make 16 layers, and each hole goes through every layer: 1 × 16 = 16.
- A 20
- B 10
- C 40
- D 9
Show answer
Why:
2 folds make 4 layers, and each hole goes through every layer: 5 × 4 = 20.
- A 6
- B 12
- C 24
- D 7
Show answer
Why:
2 folds make 4 layers, and each hole goes through every layer: 3 × 4 = 12.
- A 32
- B 8
- C 16
- D 4
Show answer
Why:
Each fold doubles the layers: 2 × 2 × 2 × 2 = 16.
- A The longest fold line
- B The first fold that was made
- C Any fold; the order does not matter
- D The last fold that was made
Show answer
Why:
The last fold is on top of the pile of layers, so it opens first.
- A At the bottom-left
- B At the top-left
- C At the top-right
- D At the bottom-right
Show answer
Why:
A vertical fold acts as a mirror: right becomes left, bottom stays bottom.
- A One half-circle hole
- B One full circular hole
- C Two half-circle holes
- D Two full circles
Show answer
Why:
The cut touches the fold, so it joins its reflection into a full circle.
- A 25
- B 10
- C 32
- D 16
Show answer
Why:
Doubling each time: 2⁵ = 32.
- A Both A and R are true, and R is the correct explanation of A
- B Both A and R are true, but R is not the correct explanation of A
- C A is true but R is false
- D A is false but R is true
Show answer
Why:
The punch passes through all 4 layers, one hole each, so R explains A (holes away from the folds).
- A Both A and R are true, and R is the correct explanation of A
- B Both A and R are true, but R is not the correct explanation of A
- C A is true but R is false
- D A is false but R is true
Show answer
Why:
R is true, and that is why A is false: a mirror image of an asymmetric hole faces the other way.
- A 1 only
- B 2 only
- C Both 1 and 2
- D Neither 1 nor 2
Show answer
Why:
2 folds → 4 layers, and 3 × 4 = 12 (holes away from the folds). Both are true.
- A 1 only
- B 2 only
- C Both 1 and 2
- D Neither 1 nor 2
Show answer
Why:
The right half does not move, so it does not change; only the left half is reflected onto it.
Important short questions (3)
Three folds make 2³ = 8 layers, and each punch goes through all 8, so 2 × 8 = 16 holes.
The last fold lies on top of the others, so it is the only one that can be opened first; each opening reflects the holes across that fold line.
It joins its mirror image across the fold, so it becomes one diamond (or a larger triangle) instead of two separate pieces.
Long answer questions (1)
Open the top-over-bottom fold first: the triangle gets a copy in the top-right quarter, reflected top to bottom.
Then open the left-over-right fold: both triangles get copies in the left half, reflected left to right.
The sheet shows 4 triangles, one near each corner, each the mirror image of its neighbours, so all four right angles point to the corners (or all to the centre).
Flashcards (12)
Play this topic
- Fold facts
Embedded Figures and Pattern Completion
Find a simple figure hidden inside a complex one in the same size and direction, find which small figure a big one hides, complete a symmetric pattern, and count lines of symmetry.
What you will be able to do
- I can trace a given figure inside a complex figure line by line.
- I can reject options that hide a flipped or turned copy.
- I can complete a pattern using its lines of symmetry.
- I can state the number of lines of symmetry of common shapes.
Key points
An embedded figure must appear in the same size and the same direction; a flipped or turned copy does not count.
Start from the most unusual part of the simple figure, such as a slanting line or a sharp corner, and look for it first.
Extra lines around the hidden figure are allowed; missing lines are not.
A line of the simple figure may lie along a longer line of the complex figure.
In pattern completion, each quarter of a pattern symmetric about both centre lines is the mirror image of its neighbour.
The diagonally opposite quarter is the 180° turn of a quarter, not its mirror image.
Lines of symmetry: square 4, rectangle 2, equilateral triangle 3, regular hexagon 6, parallelogram 0, circle infinitely many.
Full explanation
Kabir at Fatehpur Sikri
Kabir's class visits Fatehpur Sikri near Agra. The guide points to a stone jali screen and says: "There is a six-pointed star hidden in this pattern. Who can find it?" Kabir stares at hundreds of crossing lines and sees nothing. His friend Sana finds it in ten seconds.
Her secret is a method, and you will learn it here.
What counts as embedded?
Figure X is embedded in a bigger figure if every line of X is present there:
- in the same size,
- in the same direction (not flipped, not turned),
- with no line missing.
Extra lines around it do not matter.
Sana's method
- Pick the most unusual part of X: a slanting line, a sharp corner or a short step.
- Find every place in the big figure where that part appears in the same direction.
- From each such place, trace the remaining lines of X. One missing line means that place fails.
The traps in the options
Examiners make three kinds of wrong options:
- the big figure hides the mirror image of X;
- it hides X turned through 90° or 180°;
- it has X with one line missing.
So after you find a match, check its direction and count its lines.
The reverse question
Sometimes one big figure is given, and you must choose which small figure it hides. Use the same method on each option. The flipped and turned versions of the right answer are the usual distractors.
Completing a symmetric pattern
A pattern that is symmetric about both centre lines is made of four quarters:
- left and right neighbours are mirror images,
- top and bottom neighbours are water images,
- diagonally opposite quarters are 180° turns.
To fill the missing quarter, reflect its neighbour across the line between them.
Lines of symmetry
A line of symmetry is a fold line that makes the two halves match. Knowing the common counts saves time.
Exam shortcuts
- Start with the odd part of X, not the obvious square.
- Same size, same direction, every line.
- Reject mirror and turned copies at once.
- Completion: neighbours mirror, opposites turn.
- Regular n-gon: n lines of symmetry.
Back to Kabir
Sana shows Kabir her trick: "Don't look for the whole star. Look for one sharp point, then follow its two sides." Kabir tries the next jali and finds a hexagon in it before Sana does.
Mind map
The whole topic on one page.
Concepts and terms
A simple figure that forms part of a bigger figure, with every one of its lines present in the same size and direction.
Which way a figure faces. A mirror image or a rotated copy has a different orientation, so it is a different figure here.
A design with a missing part is completed by using its symmetry: the missing part is the reflection of a known part.
A line along which a figure can be folded so that the two halves match exactly.
Did you know
The stone jali screens of Fatehpur Sikri hide hundreds of small stars and hexagons inside one large symmetric pattern.
Psychologists use embedded-figure tests to measure how well people separate a shape from its background.
Memory tricks
Embedded figures — Same size, same side, every line — All three must hold for the figure to be really hidden there.
Completion — Neighbours mirror, opposites turn — Side-by-side quarters are mirror images; diagonal quarters are 180° turns.
Practice MCQs with answers (45)
- A 1
- B 2
- C 3
- D 4
Show answer
Why:
Trace X's lines inside each figure. Only figure (1) contains every line of X in the same position and direction; the others hold only a wrong copy: the mirror image of X; X turned a quarter; X upside down.
- A 1
- B 2
- C 3
- D 4
Show answer
Why:
Trace X's lines inside each figure. Only figure (2) contains every line of X in the same position and direction; the others hold only a wrong copy: the mirror image of X; X turned a quarter; X upside down.
- A 1
- B 2
- C 3
- D 4
Show answer
Why:
Trace X's lines inside each figure. Only figure (3) contains every line of X in the same position and direction; the others hold only a wrong copy: the mirror image of X; X turned a quarter; X upside down.
- A 1
- B 2
- C 3
- D 4
Show answer
Why:
Trace X's lines inside each figure. Only figure (4) contains every line of X in the same position and direction; the others hold only a wrong copy: the mirror image of X; X turned a quarter; X upside down.
- A 1
- B 2
- C 3
- D 4
Show answer
Why:
Trace X's lines inside each figure. Only figure (1) contains every line of X in the same position and direction; the others hold only a wrong copy: the mirror image of X; X turned a quarter; X upside down.
- A 1
- B 2
- C 3
- D 4
Show answer
Why:
Trace X's lines inside each figure. Only figure (2) contains every line of X in the same position and direction; the others hold only a wrong copy: the mirror image of X; X turned a quarter; X upside down.
- A 1
- B 2
- C 3
- D 4
Show answer
Why:
Trace X's lines inside each figure. Only figure (3) contains every line of X in the same position and direction; the others hold only a wrong copy: the mirror image of X; X turned a quarter; X upside down.
- A 1
- B 2
- C 3
- D 4
Show answer
Why:
Trace X's lines inside each figure. Only figure (4) contains every line of X in the same position and direction; the others hold only a wrong copy: the mirror image of X; X turned a quarter; X upside down.
- A 1
- B 2
- C 3
- D 4
Show answer
Why:
Trace X's lines inside each figure. Only figure (1) contains every line of X in the same position and direction; the others hold only a wrong copy: the mirror image of X; X turned a quarter; X upside down.
- A 1
- B 2
- C 3
- D 4
Show answer
Why:
Trace X's lines inside each figure. Only figure (2) contains every line of X in the same position and direction; the others hold only a wrong copy: the mirror image of X; X turned a quarter; X upside down.
- A 1
- B 2
- C 3
- D 4
Show answer
Why:
Trace X's lines inside each figure. Only figure (3) contains every line of X in the same position and direction; the others hold only a wrong copy: the mirror image of X; X turned a quarter; X upside down.
- A 1
- B 2
- C 3
- D 4
Show answer
Why:
Trace X's lines inside each figure. Only figure (4) contains every line of X in the same position and direction; the others hold only a wrong copy: the mirror image of X; X turned a quarter; X upside down.
- A 1
- B 2
- C 3
- D 4
Show answer
Why:
Figure (1) can be traced inside the question figure line for line. The others are the same shape flipped or turned, and no flipped or turned copy is present.
- A 1
- B 2
- C 3
- D 4
Show answer
Why:
Figure (2) can be traced inside the question figure line for line. The others are the same shape flipped or turned, and no flipped or turned copy is present.
- A 1
- B 2
- C 3
- D 4
Show answer
Why:
Figure (3) can be traced inside the question figure line for line. The others are the same shape flipped or turned, and no flipped or turned copy is present.
- A 1
- B 2
- C 3
- D 4
Show answer
Why:
Figure (4) can be traced inside the question figure line for line. The others are the same shape flipped or turned, and no flipped or turned copy is present.
- A 1
- B 2
- C 3
- D 4
Show answer
Why:
Figure (1) can be traced inside the question figure line for line. The others are the same shape flipped or turned, and no flipped or turned copy is present.
- A 1
- B 2
- C 3
- D 4
Show answer
Why:
Figure (2) can be traced inside the question figure line for line. The others are the same shape flipped or turned, and no flipped or turned copy is present.
- A 1
- B 2
- C 3
- D 4
Show answer
Why:
Figure (3) can be traced inside the question figure line for line. The others are the same shape flipped or turned, and no flipped or turned copy is present.
- A 1
- B 2
- C 3
- D 4
Show answer
Why:
Figure (4) can be traced inside the question figure line for line. The others are the same shape flipped or turned, and no flipped or turned copy is present.
- A 1
- B 2
- C 3
- D 4
Show answer
Why:
The top-right quarter must be the mirror image of the top-left quarter across the vertical centre line (and the water image of the bottom-right quarter). Figure (1) is exactly that.
- A 1
- B 2
- C 3
- D 4
Show answer
Why:
The top-right quarter must be the mirror image of the top-left quarter across the vertical centre line (and the water image of the bottom-right quarter). Figure (2) is exactly that.
- A 1
- B 2
- C 3
- D 4
Show answer
Why:
The top-right quarter must be the mirror image of the top-left quarter across the vertical centre line (and the water image of the bottom-right quarter). Figure (3) is exactly that.
- A 1
- B 2
- C 3
- D 4
Show answer
Why:
The top-right quarter must be the mirror image of the top-left quarter across the vertical centre line (and the water image of the bottom-right quarter). Figure (4) is exactly that.
- A 1
- B 2
- C 3
- D 4
Show answer
Why:
The top-right quarter must be the mirror image of the top-left quarter across the vertical centre line (and the water image of the bottom-right quarter). Figure (1) is exactly that.
- A 1
- B 2
- C 3
- D 4
Show answer
Why:
The top-right quarter must be the mirror image of the top-left quarter across the vertical centre line (and the water image of the bottom-right quarter). Figure (2) is exactly that.
- A 1
- B 2
- C 3
- D 4
Show answer
Why:
The top-right quarter must be the mirror image of the top-left quarter across the vertical centre line (and the water image of the bottom-right quarter). Figure (3) is exactly that.
- A 1
- B 2
- C 3
- D 4
Show answer
Why:
The top-right quarter must be the mirror image of the top-left quarter across the vertical centre line (and the water image of the bottom-right quarter). Figure (4) is exactly that.
- A 1
- B 2
- C 3
- D 4
Show answer
Why:
The top-right quarter must be the mirror image of the top-left quarter across the vertical centre line (and the water image of the bottom-right quarter). Figure (1) is exactly that.
- A 1
- B 2
- C 3
- D 4
Show answer
Why:
The top-right quarter must be the mirror image of the top-left quarter across the vertical centre line (and the water image of the bottom-right quarter). Figure (2) is exactly that.
- A 5
- B 3
- C 4
- D 8
Show answer
Why:
A square has 4 lines of symmetry, each of which acts like a mirror.
- A 3
- B 1
- C 4
- D 2
Show answer
Why:
A rectangle (not a square) has 2 lines of symmetry, each of which acts like a mirror.
- A 3
- B 4
- C 2
- D 6
Show answer
Why:
A equilateral triangle has 3 lines of symmetry, each of which acts like a mirror.
- A 0
- B 1
- C 4
- D 2
Show answer
Why:
A isosceles triangle (not equilateral) has 1 line of symmetry, each of which acts like a mirror.
- A 12
- B 7
- C 6
- D 5
Show answer
Why:
A regular hexagon has 6 lines of symmetry, each of which acts like a mirror.
- A 3
- B 1
- C 4
- D 2
Show answer
Why:
A rhombus (not a square) has 2 lines of symmetry, each of which acts like a mirror.
- A 0
- B 1
- C 2
- D 4
Show answer
Why:
A parallelogram (not a rectangle or rhombus) has 0 lines of symmetry; no fold makes its halves match.
- A 6
- B 5
- C 4
- D 10
Show answer
Why:
A regular pentagon has 5 lines of symmetry, each of which acts like a mirror.
- A The same triangle whose base lies on a longer line
- B The same triangle in a corner of the figure
- C A same-size triangle with its right angle at the bottom-right
- D The same triangle with extra lines crossing it
Show answer
Why:
Moving the right angle to the bottom-right is a mirror image: the direction has changed.
- A A mirror image
- B A water image
- C A plain copy
- D A 180° turn
Show answer
Why:
Reflect across the vertical line, then across the horizontal line: two flips make a 180° turn.
- A 6
- B 8
- C 12
- D 3
Show answer
Why:
A regular n-gon has n lines of symmetry, so the hexagon has 6.
- A Both A and R are true, and R is the correct explanation of A
- B Both A and R are true, but R is not the correct explanation of A
- C A is true but R is false
- D A is false but R is true
Show answer
Why:
Both true, and R is the rule that makes A true.
- A Both A and R are true, and R is the correct explanation of A
- B Both A and R are true, but R is not the correct explanation of A
- C A is true but R is false
- D A is false but R is true
Show answer
Why:
R is true, but a rectangle's diagonals are not lines of symmetry; it has only 2 (the midlines). A is false.
- A 1 only
- B 2 only
- C Both 1 and 2
- D Neither 1 nor 2
Show answer
Why:
The hexagon has 6; such a parallelogram has none.
- A 1 only
- B 2 only
- C Both 1 and 2
- D Neither 1 nor 2
Show answer
Why:
Extra lines are allowed, but the size must be the same, so statement 2 is false.
Important short questions (3)
Every line of X must be in Y, in the same size and in the same direction.
Reflect the top-left quarter across the vertical centre line (or the bottom-right quarter across the horizontal one).
Folding along a midline matches the halves, but folding along a diagonal does not, because the sides are unequal.
Long answer questions (1)
Pick the most unusual part of X. In each figure, find where that part appears in the same direction. From there, trace every remaining line of X; all must be present.
Wrong options usually hide the mirror image of X, a turned copy of X, or X with one line missing. Reject them by checking direction and counting lines.
Flashcards (12)
Play this topic
- Hidden or not?
Veda Skills Logical Reasoning Unit 17 — frequently asked questions
Write the letters in reverse order, then flip every letter left to right. Letters such as A, H, M, O, T stay the same.
11:60 − 5:35 = 6:25.
H, I, O and X, because each has both a vertical and a horizontal line of symmetry.
Three folds make 2³ = 8 layers, and each punch goes through all 8, so 2 × 8 = 16 holes.
The last fold lies on top of the others, so it is the only one that can be opened first; each opening reflects the holes across that fold line.
It joins its mirror image across the fold, so it becomes one diamond (or a larger triangle) instead of two separate pieces.
Every line of X must be in Y, in the same size and in the same direction.
Reflect the top-left quarter across the vertical centre line (or the bottom-right quarter across the horizontal one).
Folding along a midline matches the halves, but folding along a diagonal does not, because the sides are unequal.
All Veda Skills Logical Reasoning units
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