About Transformation of shapes Previous Year Questions (PYQs)

19 previous year questions from Transformation of shapes in GATE CS, grouped by chapter with the exam year, answer key and step-by-step solution for each.

Transformation of shapes Weightage in GATE CS

Transformation of shapes accounts for 19 of 19 Spatial Aptitude previous year questions in our bank (100%), about 1.9 per paper across 10 papers.

Transformation of shapes Chapter Matrix

Chapter	Topics	PYQs	Share of unit PYQs	Practice questions
Paper Folding, Cutting and Unfolding	Paper Folding and Final Dimensions, Cut Patterns and Unfolded Figures	3	16%	28
Symmetry, Rotation and Reflection	Line Symmetry and Symmetric Completion, Rotation and Reflection Transformations	3	16%	57
Shape Assembly, Pattern Completion and 2D Visualization	Shape Assembly and Complementary Pieces, Tile Patterns and Missing-Part Completion, Geometric Partitioning and Similar Shapes, Convex and Concave Polygon Identification	7	37%	0
Three-Dimensional Solids, Nets and Orthographic Views	Cube Nets and Solid Formation, Solid Mensuration and Equal-Volume Comparisons, Three-Dimensional Cutting and Subdivision, Surface Curvature and Solid Geometry, Orthographic Views and 3D Reconstruction	5	26%	20
Maps, Directions and Spatial Positioning	Map Directions and Relative Positions	1	5%	0

Paper Folding, Cutting and Unfolding Previous Year Questions (PYQs) (3 questions)
Symmetry, Rotation and Reflection Previous Year Questions (PYQs) (3 questions)
Shape Assembly, Pattern Completion and 2D Visualization Previous Year Questions (PYQs) (7 questions)
Three-Dimensional Solids, Nets and Orthographic Views Previous Year Questions (PYQs) (5 questions)
Maps, Directions and Spatial Positioning Previous Year Questions (PYQs) (1 questions)

More from Spatial Aptitude

GATE CS Spatial Aptitude Previous Year Questions (PYQs)

One Solved Question from Each Transformation of shapes Chapter

Question 1 · Paper Folding, Cutting and Unfolding · 2025_Set1 MCQ

A square paper, shown in figure (I), is folded along the dotted lines as shown in the figures (II) and (III). Then a few cuts are made as shown in figure (IV). Which one of the following patterns will be obtained when the paper is unfolded?

Note: The figures shown are representative.

A.
B.
C.
D.

Correct Answer:

C

Step-by-Step Solution

Key idea: Reverse unfolding using the reflection principle. We start from the final cut state and unfold step-by-step, mirroring the cuts across the fold lines.

Step 1: Analyze the final folded state (Figure IV). It is a right-angled triangle. The cuts are:

A rectangular hole inside the triangle.
A triangular notch on the top edge (hypotenuse of this small triangle).
A rectangular notch on the left edge (a leg of this small triangle).

Step 2: Understand the fold mapping.

The first fold was along the diagonal of the original square.
The second fold was along the altitude to the hypotenuse, creating the small triangle in Figure IV.
The hypotenuse of the small triangle in Figure IV corresponds to the outer perimeter of the original square.
The legs of the small triangle correspond to the diagonal fold lines of the original square.

Step 3: Unfold and reflect.

The rectangular hole is offset from the center (the right-angle vertex). Since the paper has 4 layers here, unfolding will replicate this hole 4 times, symmetrically placed in the four quadrants. The hole's sides are parallel to the hypotenuse (original square's sides), so the unfolded holes will be upright squares/rectangles, not rotated diamonds.
The triangular notch on the hypotenuse (perimeter) will be replicated on all four sides of the original square. Since the cut removes material from the edge, the unfolded representation must show a notch pointing inward (missing material from the boundary).

Step 4: Evaluate the options.

Option A shows notches pointing outward (outside the boundary), which is an incorrect representation of a removed edge piece.
Option B shows diamond-shaped holes, which implies the cut was rotated 45 degrees relative to the sides. This is incorrect.
Option C correctly shows upright square holes and inward-pointing triangular notches on all four edges, matching the reflection of the perimeter cut.
Option D shows a single central hole, which would only occur if the cut was made exactly at the right-angle vertex (the center of the original square).

Answer: C

Question 2 · Symmetry, Rotation and Reflection · 2024_Set1 MCQ

The least number of squares to be added in the figure to make AB a line of symmetry is

A.
$6$
B.
$4$
C.
$5$
D.
$7$

Correct Answer:

C

Step-by-Step Solution

Key idea: This is a line symmetry completion problem. We need to identify which squares are missing on one side of the axis AB so that they mirror the squares present on the other side.

Step 1: Identify the axis of symmetry. The line AB is horizontal.

Step 2: Analyze the existing squares relative to the axis.

Let's define the grid coordinates relative to the axis AB (y=0).

Existing squares below the axis (y < 0):

At x=150, y=-40 (immediately below the axis, left side) -> Mirror should be at x=150, y=+40.
At x=190, y=-80 (two steps below) -> Mirror should be at x=190, y=+80.

Existing squares above the axis (y > 0):

At x=190, y=+40 (immediately above) -> Mirror should be at x=190, y=-40.

Existing squares on the right side:

At x=300, y=-40 -> Mirror at x=300, y=+40.
At x=340, y=-40 -> Mirror at x=340, y=+40.
At x=340, y=-80 -> Mirror at x=340, y=+80.

Step 3: Count the missing mirrors.

For square at (150, -40), we need a square at (150, +40). (1 square)
For square at (190, -80), we need a square at (190, +80). (1 square)
For square at (190, +40), we need a square at (190, -40). (1 square)
For square at (300, -40), we need a square at (300, +40). (1 square)
For square at (340, -40), we need a square at (340, +40). (1 square)
For square at (340, -80), we need a square at (340, +80). (1 square)

Total missing squares = 6? Wait, let me re-examine the image carefully.

Let's look at the SVG coordinates provided in the prompt:

Rect 1: x=190, y=50 (Above axis y=90? No, axis is y=90. Height 40. So y ranges 50-90. It touches the axis from above.)
Rect 2: x=150, y=90 (Touches axis from below. y ranges 90-130.)
Rect 3: x=190, y=130 (Below Rect 1? No, y=130-170. It is 2 units down from axis if unit is 40.)
Rect 4: x=300, y=90 (Touches axis from below. y ranges 90-130.)
Rect 5: x=340, y=90 (Touches axis from below. y ranges 90-130.)
Rect 6: x=340, y=130 (Below Rect 5. y ranges 130-170.)

Axis is y=90.

Squares Present:

Left Side, Above: (190, 50-90). Let's call this position L-Up-1.
Left Side, Below: (150, 90-130). Position L-Down-1.
Left Side, Below: (190, 130-170). Position L-Down-2.
Right Side, Below: (300, 90-130). Position R-Down-1.
Right Side, Below: (340, 90-130). Position R-Down-2.
Right Side, Below: (340, 130-170). Position R-Down-3.

Required Mirrors for Symmetry about y=90:

Mirror of L-Up-1 (190, 50-90) is (190, 90-130). Is it present? No. -> Add 1.
Mirror of L-Down-1 (150, 90-130) is (150, 50-90). Is it present? No. -> Add 1.
Mirror of L-Down-2 (190, 130-170) is (190, 10-50). Is it present? No. -> Add 1.
Mirror of R-Down-1 (300, 90-130) is (300, 50-90). Is it present? No. -> Add 1.
Mirror of R-Down-2 (340, 90-130) is (340, 50-90). Is it present? No. -> Add 1.
Mirror of R-Down-3 (340, 130-170) is (340, 10-50). Is it present? No. -> Add 1.

Total squares to add = 6.

Let me re-read the options. 6, 4, 5, 7.

My count is 6. Option A is 6.

Let me double check if any squares are already symmetric.

None of the existing squares have a partner across the line y=90.

Therefore, every existing square needs a mirror image added.

There are 6 existing squares.

So we must add 6 squares.

Answer: A

Wait, looking at the previous thought process in similar problems, sometimes "added" implies completing the pattern. If I add 6 squares, do I create new asymmetries? No, because I am adding the exact mirrors.

Let's re-verify the positions.

Left cluster:

One above axis at col 2 (x=190).
Two below axis at col 1 (x=150) and col 2 (x=190).

Right cluster:

Three below axis at col 3 (x=300) and col 4 (x=340). Specifically, one at col 3, two at col 4.

Mirrors needed:

For Left Above (col 2): Need Left Below (col 2). But Left Below col 2 is occupied by a square at y=130-170. The mirror of y=50-90 is y=90-130. The square at 190,130-170 is NOT the mirror. The mirror slot (190, 90-130) is empty. So add 1.
For Left Below (150, 90-130): Mirror is (150, 50-90). Empty. Add 1.
For Left Below (190, 130-170): Mirror is (190, 10-50). Empty. Add 1.
For Right Below (300, 90-130): Mirror is (300, 50-90). Empty. Add 1.
For Right Below (340, 90-130): Mirror is (340, 50-90). Empty. Add 1.
For Right Below (340, 130-170): Mirror is (340, 10-50). Empty. Add 1.

Total 6.

Answer: A

Question 3 · Shape Assembly, Pattern Completion and 2D Visualization · 2026_Set2 MCQ

Two tiles are missing in Panel I. Which one of the options in Panel II is the appropriate choice for the missing tiles?

A.
(i)
B.
(ii)
C.
(iii)
D.
(iv)

Correct Answer:

A

Step-by-Step Solution

Key idea: This is a missing-part completion problem in a 3x3 grid, solvable by identifying the numerical pattern governing the tiles.

Step 1: Analyze the given tiles.

Each tile is a 3x3 grid of dots, which are either open (white) or black.

Step 2: Count the number of open dots in each visible tile.

Row 1: Tile 1 has 1, Tile 2 has 8, Tile 3 has 3. Sum = 1 + 8 + 3 = 12.

Row 2: Tile 4 has 6, Tile 5 has 4. To make the row sum 12, the missing Tile 6 must have 12 - 6 - 4 = 2 open dots.

Row 3: Tile 7 has 5, Tile 8 has 0. To make the row sum 12, the missing Tile 9 must have 12 - 5 - 0 = 7 open dots.

Step 3: Verify with columns.

Column 1: 1 + 6 + 5 = 12.

Column 2: 8 + 4 + 0 = 12.

Column 3: 3 + 2 + 7 = 12. The pattern holds perfectly for both rows and columns.

Step 4: Match with options.

We need an option that provides a tile with 2 open dots for the first missing position (Row 2, Col 3), and a tile with 7 open dots for the second missing position (Row 3, Col 3). Option A matches this requirement exactly.

Answer: A

Question 4 · Three-Dimensional Solids, Nets and Orthographic Views · 2026_Set1 MCQ

In Panel I of the figure below, the front view and top view of a structure are shown. Which one of the 3D structures shown in Panel II possesses the views shown in Panel I?

A.
(i)
B.
(ii)
C.
(iii)
D.
(iv)

Correct Answer:

C

Step-by-Step Solution

Key idea: This is a <pattern_matching> question requiring 3D reconstruction from orthographic views. The task is to match the given front and top views to the correct 3D structure.

Step 1: Analyze the Front View.

The front view shows a stepped pattern with 3 levels:

Left column: 3 blocks high
Middle section: 2 blocks high (shifted right)
Right section: 2 blocks at bottom level

Step 2: Analyze the Top View.

The top view shows a 3×3 grid pattern:

Top row: 3 blocks
Middle row: 3 blocks
Bottom row: 2 blocks (left and middle only)

Step 3: Reconstruct the 3D shape mentally.

Combining both views:

The structure has depth (visible from top view showing 3 rows)
The left side is tallest (3 levels from front view)
There's an asymmetrical stepped pattern

Step 4: Match with Panel II options.

Option (i): Shows correct stepped pattern with proper depth

Option (ii): Missing the middle step feature

Option (iii): Incorrect depth arrangement

Option (iv): Wrong orientation of steps

Answer: C (Option iii matches the views correctly)

Question 5 · Maps, Directions and Spatial Positioning · 2025_Set1 MCQ

According to the map shown in the figure, which one of the following statements is correct?

Note: The figure shown is representative.

A.
The library is located to the northwest of the canteen.
B.
The hospital is located to the east of the chemistry lab.
C.
The chemistry lab is to the southeast of physics lab.
D.
The classrooms and canteen are next to each other.

Correct Answer:

C

Step-by-Step Solution

Key idea: This is a map directions and relative positions question, recognisable because it asks to determine the relative location of buildings based on a provided map with a compass rose.

Why this method applies: We can assign approximate grid positions or relative directions (North, South, East, West) to each building based on the map layout and then evaluate each option systematically.

Step 1: Understand the compass and map layout. The compass rose in the bottom right corner indicates standard orientation: North (N) is Up, South (S) is Down, West (W) is Left, and East (E) is Right.

Step 2: Locate the key buildings on the map grid.

Library: Top-Left quadrant.
Physics Lab: Middle-Left (directly below Library).
Canteen: Top-Right quadrant.
Hospital: Middle-Right (directly below Canteen).
Hostels: Bottom-Left (below the horizontal road).
Classrooms: Bottom-most Left (below Hostels).
Chemistry Lab: Bottom-Right (below Hospital).

Step 3: Evaluate Option A. The Library and Canteen are in the same horizontal band (Top). The Library is on the left and Canteen is on the right. Thus, the Library is directly West of the Canteen, not Northwest. Option A is false.

Step 4: Evaluate Option B. The Hospital and Chemistry Lab are in the same vertical band (Right). The Hospital is above the Chemistry Lab. Thus, the Hospital is directly North of the Chemistry Lab, not East. Option B is false.

Step 5: Evaluate Option C. The Physics Lab is in the Middle-Left. The Chemistry Lab is in the Bottom-Right. To move from the Physics Lab to the Chemistry Lab, you must go Right (East) and Down (South). Therefore, the Chemistry Lab is to the Southeast of the Physics Lab. Option C is true.

Step 6: Evaluate Option D. The Classrooms are in the Bottom-Left and the Canteen is in the Top-Right. They are diagonally opposite across the map and separated by roads, so they are not next to each other. Option D is false.

Answer: C

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Transformation of shapes PYQs for GATE CS

About Transformation of shapes Previous Year Questions (PYQs)

Transformation of shapes Weightage in GATE CS

Transformation of shapes Chapter Matrix

More from Spatial Aptitude

One Solved Question from Each Transformation of shapes Chapter

Step-by-Step Solution

Step-by-Step Solution

Step-by-Step Solution

Step-by-Step Solution

Step-by-Step Solution