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Figure Analogy - Beginner-Intermediate Level: shape transformations BEGINNER-INTERMEDIATE

Comprehensive race against clock worksheet covering 20 beginner-intermediate-level figure analogy problems. Worksheet 8 of 30 emphasizes shape transformations. Master visual analogies, shape relationships, image analogies through detailed explanations. Difficulty: building on fundamentals with moderate challenges. Tailored for developing preparation.

📝 Worksheet 8 of 30 • 20 questions • ⏱️ Estimated time: 20 minutes • 🎯 Beginner-intermediate level

What you'll learn in this worksheet:
Your progress through Figure Analogy
Worksheet 8 of 30 (26% complete)

Question 1

Figure Analogy: A : B :: C : ? Figure A is reflected across a horizontal axis to become Figure B. Apply the same mirror reflection to Figure C to find '?'.
Step-by-Step Solution:

STEP 1: Identify Mirror Axis
- Compare A and B: They are mirror images
- Mirror axis: Horizontal

STEP 2: Properties of horizontal Mirror
- Horizontal mirror: Left ↔ Right swap
- All horizontal positions inverted
- Vertical positions unchanged

STEP 3: Apply to Figure C
- Reflect C across horizontal axis
- Maintain shape type
- Invert orientation

Answer: Figure mirrored across horizontal axis (mirror image of C)
reflection, mirror, axis-symmetry

Question 2

Figure Analogy: A : B :: C : ? Figure A is reflected across a vertical axis to become Figure B. Apply the same mirror reflection to Figure C to find '?'.
Step-by-Step Solution:

STEP 1: Identify Mirror Axis
- Compare A and B: They are mirror images
- Mirror axis: Vertical

STEP 2: Properties of vertical Mirror
- Vertical mirror: Left ↔ Right swap
- All horizontal positions inverted
- Vertical positions unchanged

STEP 3: Apply to Figure C
- Reflect C across vertical axis
- Maintain shape type
- Invert orientation

Answer: Figure mirrored across vertical axis (mirror image of C)
reflection, mirror, axis-symmetry

Question 3

Figure Analogy: A : B :: C : ? In A→B, elements swap positions (left element moves right, right element moves left). Apply to C.
Step-by-Step Solution:

STEP 1: Map Element Positions in A
- Container: Square
- Element 1 (Circle): Left portion of square
- Element 2 (Triangle): Right portion of square
- Spatial arrangement: Circle | Triangle (left | right)

STEP 2: Map Element Positions in B
- Container: Square (same)
- Element 1 (Triangle): Left portion of square
- Element 2 (Circle): Right portion of square
- Spatial arrangement: Triangle | Circle (left | right)

STEP 3: Identify Transformation Type
- Container: Unchanged (square remains square)
- Element types: Unchanged (circle and triangle still present)
- Element positions: Swapped (exchanged positions)
- Transformation: Positional swap/exchange

STEP 4: Identify Elements in C
- Container: Circle
- Element 1 (Square): Left portion of circle
- Element 2 (Line): Right portion of circle
- Current arrangement: Square | Line (left | right)

STEP 5: Apply Position Swap to C
- Element 1 (Square): Moves from left → right
- Element 2 (Line): Moves from right → left
- Result arrangement: Line | Square (left | right)
- Container: Remains circle (unchanged)

Answer: Circle with line on left portion and square on right portion (positions swapped)
position-swap, spatial, element-exchange

Question 4

Figure Analogy: A : B :: C : ? Figure A has 1 dot(s). Figure B has 3 dot(s) (2 more). Apply the same transformation to Figure C.
Step-by-Step Solution:

STEP 1: Identify Numerical Pattern
- A: 1 dot(s)
- B: 3 dot(s)
- Change: +2 dot(s) added

STEP 2: Apply to Figure C
- C: 1 dot(s) (different container)
- Add 2 more dot(s)
- Result: 3 dots total

Answer: Square with 3 dots (2 more than original)
quantitative, progression, element-addition

Question 5

Figure Analogy: A : B :: C : ? In A→B, the inner square becomes a circle (matching the outer circle's shape). Apply the same transformation to C.
Step-by-Step Solution:

STEP 1: Identify Transformation Rule
- A: Circle (outer) + Square (inner)
- B: Circle (outer) + Circle (inner)
- Rule: Inner shape transforms to match outer shape type

STEP 2: Apply to Figure C
- C: Triangle (outer) + Square (inner)
- Transform inner square to match outer triangle
- Result: Triangle with inscribed triangle

Answer: Square with inscribed square (inner becomes square)
shape-change, morphing, property-matching

Question 6

Figure Analogy: A : B :: C : ? A→B: Rotated 45° clockwise + scaled 1.3x + colors inverted. Apply all three to C.
Step-by-Step Solution:

STEP 1: Identify First Transformation - Rotation
- Figure A: Diamond (square rotated 45°)
- Figure B: Diamond rotated further (additional 45° clockwise)
- First transformation: 45° clockwise rotation

STEP 2: Identify Second Transformation - Scaling
- Measure A diagonal span: Approximately 36 units
- Measure B diagonal span: Approximately 48 units
- Calculate ratio: 48/36 ≈ 1.33 (approximately 1.3)
- Second transformation: 1.3× scaling (30% enlargement)

STEP 3: Identify Third Transformation - Color Inversion
- Figure A fill: White (light), dot: Black (dark)
- Figure B fill: Black (dark), dot: White (light)
- Third transformation: Complete color/shading inversion

STEP 4: Analyze Figure C
- Shape: Rectangle (horizontal orientation)
- Size: Standard (40×34 units)
- Colors: White background, black internal lines
- Internal elements: 2 perpendicular lines (cross pattern)

STEP 5: Apply Transformations in Sequence
- Rotate 45° clockwise → Rectangle becomes tilted (diamond-like)
- Scale 1.3× → All dimensions multiplied by 1.3
- Invert colors → Black background, white lines

Answer: Rectangle rotated 45° clockwise, dimensions enlarged by 1.3×, with inverted coloring (black fill with white cross lines inside)
multi-step, complex, three-transformations

Question 7

Figure Analogy: A : B :: C : ? In A→B, the inner square becomes a circle (matching the outer circle's shape). Apply the same transformation to C.
Step-by-Step Solution:

STEP 1: Identify Transformation Rule
- A: Circle (outer) + Square (inner)
- B: Circle (outer) + Circle (inner)
- Rule: Inner shape transforms to match outer shape type

STEP 2: Apply to Figure C
- C: Triangle (outer) + Square (inner)
- Transform inner square to match outer triangle
- Result: Triangle with inscribed triangle

Answer: Circle with inscribed circle (inner becomes circle)
shape-change, morphing, property-matching

Question 8

Figure Analogy: A : B :: C : ? Figure A has 1 dot(s). Figure B has 3 dot(s) (2 more). Apply the same transformation to Figure C.
Step-by-Step Solution:

STEP 1: Identify Numerical Pattern
- A: 1 dot(s)
- B: 3 dot(s)
- Change: +2 dot(s) added

STEP 2: Apply to Figure C
- C: 1 dot(s) (different container)
- Add 2 more dot(s)
- Result: 3 dots total

Answer: Circle with 3 dots (2 more than original)
quantitative, progression, element-addition

Question 9

Figure Analogy: A : B :: C : ? In A→B, elements swap positions (left element moves right, right element moves left). Apply to C.
Step-by-Step Solution:

STEP 1: Map Element Positions in A
- Container: Square
- Element 1 (Circle): Left portion of square
- Element 2 (Triangle): Right portion of square
- Spatial arrangement: Circle | Triangle (left | right)

STEP 2: Map Element Positions in B
- Container: Square (same)
- Element 1 (Triangle): Left portion of square
- Element 2 (Circle): Right portion of square
- Spatial arrangement: Triangle | Circle (left | right)

STEP 3: Identify Transformation Type
- Container: Unchanged (square remains square)
- Element types: Unchanged (circle and triangle still present)
- Element positions: Swapped (exchanged positions)
- Transformation: Positional swap/exchange

STEP 4: Identify Elements in C
- Container: Circle
- Element 1 (Square): Left portion of circle
- Element 2 (Line): Right portion of circle
- Current arrangement: Square | Line (left | right)

STEP 5: Apply Position Swap to C
- Element 1 (Square): Moves from left → right
- Element 2 (Line): Moves from right → left
- Result arrangement: Line | Square (left | right)
- Container: Remains circle (unchanged)

Answer: Circle with line on left portion and square on right portion (positions swapped)
position-swap, spatial, element-exchange

Question 10

Figure Analogy: A : B :: C : ? Figure A undergoes two transformations to become B: rotated 90° anticlockwise AND enlarged by 1.5x. Apply both to C.
Step-by-Step Solution:

STEP 1: Identify First Transformation (Rotation)
- Figure A orientation: Triangle pointing right
- Figure B orientation: Triangle pointing upward
- First transformation: 90° anticlockwise rotation

STEP 2: Identify Second Transformation (Scaling)
- Measure A dimensions: Small triangle (base ≈ 20 units)
- Measure B dimensions: Larger triangle (base ≈ 30 units)
- Second transformation: 1.5× scaling (enlargement by 50%)

STEP 3: Determine Transformation Sequence
- Method 1: Rotate first, then scale
- Method 2: Scale first, then rotate
- Result: Same final figure (transformations commute)
- Standard approach: Rotate, then scale

STEP 4: Apply Rotation to C (90° anticlockwise)
- Original C: Vertical rectangle (height > width)
- After rotation: Horizontal rectangle (width > height)
- Internal dot: Rotates with figure to new position

STEP 5: Apply Scaling to Rotated C (1.5×)
- Current dimensions: Already rotated rectangle
- Apply 1.5× to both length and width
- Internal dot: Maintains relative position, scales proportionally

STEP 6: Verify Combined Transformation
- Original: Vertical rectangle, small size, dot at top
- After rotation: Horizontal rectangle, small size, dot on left
- After scaling: Horizontal rectangle, 1.5× larger, dot on left (scaled position)

Answer: Rectangle in horizontal orientation (rotated 90° anticlockwise), dimensions increased by 1.5×, with dot repositioned according to both transformations
multi-step, rotation, scaling, combined-transformation

Question 11

Figure Analogy: A : B :: C : ? A→B: Rotated 45° clockwise + scaled 1.3x + colors inverted. Apply all three to C.
Step-by-Step Solution:

STEP 1: Identify First Transformation - Rotation
- Figure A: Diamond (square rotated 45°)
- Figure B: Diamond rotated further (additional 45° clockwise)
- First transformation: 45° clockwise rotation

STEP 2: Identify Second Transformation - Scaling
- Measure A diagonal span: Approximately 36 units
- Measure B diagonal span: Approximately 48 units
- Calculate ratio: 48/36 ≈ 1.33 (approximately 1.3)
- Second transformation: 1.3× scaling (30% enlargement)

STEP 3: Identify Third Transformation - Color Inversion
- Figure A fill: White (light), dot: Black (dark)
- Figure B fill: Black (dark), dot: White (light)
- Third transformation: Complete color/shading inversion

STEP 4: Analyze Figure C
- Shape: Rectangle (horizontal orientation)
- Size: Standard (40×34 units)
- Colors: White background, black internal lines
- Internal elements: 2 perpendicular lines (cross pattern)

STEP 5: Apply Transformations in Sequence
- Rotate 45° clockwise → Rectangle becomes tilted (diamond-like)
- Scale 1.3× → All dimensions multiplied by 1.3
- Invert colors → Black background, white lines

Answer: Rectangle rotated 45° clockwise, dimensions enlarged by 1.3×, with inverted coloring (black fill with white cross lines inside)
multi-step, complex, three-transformations

Question 12

Figure Analogy: A : B :: C : ? In A→B, the inner square becomes a circle (matching the outer circle's shape). Apply the same transformation to C.
Step-by-Step Solution:

STEP 1: Identify Transformation Rule
- A: Circle (outer) + Square (inner)
- B: Circle (outer) + Circle (inner)
- Rule: Inner shape transforms to match outer shape type

STEP 2: Apply to Figure C
- C: Triangle (outer) + Square (inner)
- Transform inner square to match outer triangle
- Result: Triangle with inscribed triangle

Answer: Triangle with inscribed triangle (inner becomes triangle)
shape-change, morphing, property-matching

Question 13

Figure Analogy: A : B :: C : ? Figure A undergoes two transformations to become B: rotated 90° anticlockwise AND enlarged by 1.5x. Apply both to C.
Step-by-Step Solution:

STEP 1: Identify First Transformation (Rotation)
- Figure A orientation: Triangle pointing right
- Figure B orientation: Triangle pointing upward
- First transformation: 90° anticlockwise rotation

STEP 2: Identify Second Transformation (Scaling)
- Measure A dimensions: Small triangle (base ≈ 20 units)
- Measure B dimensions: Larger triangle (base ≈ 30 units)
- Second transformation: 1.5× scaling (enlargement by 50%)

STEP 3: Determine Transformation Sequence
- Method 1: Rotate first, then scale
- Method 2: Scale first, then rotate
- Result: Same final figure (transformations commute)
- Standard approach: Rotate, then scale

STEP 4: Apply Rotation to C (90° anticlockwise)
- Original C: Vertical rectangle (height > width)
- After rotation: Horizontal rectangle (width > height)
- Internal dot: Rotates with figure to new position

STEP 5: Apply Scaling to Rotated C (1.5×)
- Current dimensions: Already rotated rectangle
- Apply 1.5× to both length and width
- Internal dot: Maintains relative position, scales proportionally

STEP 6: Verify Combined Transformation
- Original: Vertical rectangle, small size, dot at top
- After rotation: Horizontal rectangle, small size, dot on left
- After scaling: Horizontal rectangle, 1.5× larger, dot on left (scaled position)

Answer: Rectangle in horizontal orientation (rotated 90° anticlockwise), dimensions increased by 1.5×, with dot repositioned according to both transformations
multi-step, rotation, scaling, combined-transformation

Question 14

Figure Analogy: A : B :: C : ? In A→B, the inner square becomes a circle (matching the outer circle's shape). Apply the same transformation to C.
Step-by-Step Solution:

STEP 1: Identify Transformation Rule
- A: Circle (outer) + Square (inner)
- B: Circle (outer) + Circle (inner)
- Rule: Inner shape transforms to match outer shape type

STEP 2: Apply to Figure C
- C: Triangle (outer) + Square (inner)
- Transform inner square to match outer triangle
- Result: Triangle with inscribed triangle

Answer: Square with inscribed square (inner becomes square)
shape-change, morphing, property-matching

Question 15

Figure Analogy: A : B :: C : ? Figure A is enlarged by 2× to become Figure B. What should Figure '?' look like when the same scaling is applied to Figure C?
Step-by-Step Solution:

STEP 1: Identify the Scaling Factor
- Figure A circle: 20 units
- Figure B circle: 40 units
- Scaling factor = 40/20 = 2

STEP 2: Apply to Figure C
- Figure C: Square
- Apply scaling factor 2
- New dimensions = original × 2

STEP 3: Verify
- Shape type preserved ✓
- Proportions preserved ✓
- Only size changed ✓

Answer: Square enlarged by 2×
scaling, size-change, proportional

Question 16

Figure Analogy: A : B :: C : ? Figure A has 1 dot. Figure B has 2 dots (1 more). Apply the same transformation to Figure C.
Step-by-Step Solution:

STEP 1: Count Elements in A and B
- Figure A: Square + 1 dot
- Figure B: Square + 2 dots
- Change: +1 dots added

STEP 2: Apply to Figure C
- Figure C: Different container + 1 dot
- Add 1 more dots
- Result: Container + 2 dots total

Answer: Circle with 2 dots (1 original + 1 added)
element-count, addition, quantitative

Question 17

Figure Analogy: A : B :: C : ? In A→B, elements swap positions (left element moves right, right element moves left). Apply to C.
Step-by-Step Solution:

STEP 1: Map Element Positions in A
- Container: Square
- Element 1 (Circle): Left portion of square
- Element 2 (Triangle): Right portion of square
- Spatial arrangement: Circle | Triangle (left | right)

STEP 2: Map Element Positions in B
- Container: Square (same)
- Element 1 (Triangle): Left portion of square
- Element 2 (Circle): Right portion of square
- Spatial arrangement: Triangle | Circle (left | right)

STEP 3: Identify Transformation Type
- Container: Unchanged (square remains square)
- Element types: Unchanged (circle and triangle still present)
- Element positions: Swapped (exchanged positions)
- Transformation: Positional swap/exchange

STEP 4: Identify Elements in C
- Container: Circle
- Element 1 (Square): Left portion of circle
- Element 2 (Line): Right portion of circle
- Current arrangement: Square | Line (left | right)

STEP 5: Apply Position Swap to C
- Element 1 (Square): Moves from left → right
- Element 2 (Line): Moves from right → left
- Result arrangement: Line | Square (left | right)
- Container: Remains circle (unchanged)

Answer: Circle with line on left portion and square on right portion (positions swapped)
position-swap, spatial, element-exchange

Question 18

Figure Analogy: A : B :: C : ? Figure A is reflected across a horizontal axis to become Figure B. Apply the same mirror reflection to Figure C to find '?'.
Step-by-Step Solution:

STEP 1: Identify Mirror Axis
- Compare A and B: They are mirror images
- Mirror axis: Horizontal

STEP 2: Properties of horizontal Mirror
- Horizontal mirror: Left ↔ Right swap
- All horizontal positions inverted
- Vertical positions unchanged

STEP 3: Apply to Figure C
- Reflect C across horizontal axis
- Maintain shape type
- Invert orientation

Answer: Figure mirrored across horizontal axis (mirror image of C)
reflection, mirror, axis-symmetry

Question 19

Figure Analogy: A : B :: C : ? A shows circle UNION square, B shows their combined region. C shows hexagon + trapezoid. What is the union?
Step-by-Step Solution:

STEP 1: Understand Set Operation in A
- Component 1: Circle
- Operation symbol: + (indicates union/combination)
- Component 2: Rectangle
- Components: Overlapping or adjacent

STEP 2: Analyze Result in B
- Single unified region combining both shapes
- Overlapping area counted once (not double-shaded)
- Boundary: Outer perimeter of combined shape
- Operation: UNION (∪) in set theory = Combined area

STEP 3: Identify Components in C
- Component 1: Hexagon
- Operation symbol: + (same as in A)
- Component 2: Trapezoid
- Relationship: Adjacent or overlapping

STEP 4: Construct Union of C
- Merge hexagon and trapezoid
- Create single continuous region
- Outer boundary: Traces perimeter of combined shape
- Interior: All area covered by either polygon

Answer: Single merged region containing all area covered by either hexagon or trapezoid
set-operations, union, geometric-logic

Question 20

Figure Analogy: A : B :: C : ? In A→B, the inner square becomes a circle (matching the outer circle's shape). Apply the same transformation to C.
Step-by-Step Solution:

STEP 1: Identify Transformation Rule
- A: Circle (outer) + Square (inner)
- B: Circle (outer) + Circle (inner)
- Rule: Inner shape transforms to match outer shape type

STEP 2: Apply to Figure C
- C: Triangle (outer) + Square (inner)
- Transform inner square to match outer triangle
- Result: Triangle with inscribed triangle

Answer: Triangle with inscribed triangle (inner becomes triangle)
shape-change, morphing, property-matching
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