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Figure Analogy - Intermediate-Advanced Level: design analogies INTERMEDIATE-ADVANCED

Intensive strategic solving 🎯 drill: 20 intermediate-advanced-level figure analogy questions. Worksheet 20 of 30 hones your design analogies abilities. Practice figure mapping, visual parallels, shape transformations under timed conditions. Best for advanced developing students seeking advanced concepts with increasing complexity.

📝 Worksheet 20 of 30 • 20 questions • ⏱️ Estimated time: 20 minutes • 🎯 Intermediate-advanced level

What you'll learn in this worksheet:
Your progress through Figure Analogy
Worksheet 20 of 30 (66% complete)

Question 1

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 2

Figure Analogy: A : B :: C : ? Figure A is rotated 180° to become Figure B. Apply the same 180° rotation to Figure C.
Step-by-Step Solution:

STEP 1: Identify Rotation Angle
- A and B: 180° rotation (half turn)
- Every point moves to opposite side

STEP 2: Apply to Figure C
- Rotate C 180° around its center
- Shape preserved, orientation inverted
- Dot moves to opposite position

Answer: Diamond rotated 180° (upside down) with dot repositioned
rotation, inversion, complex-orientation

Question 3

Figure Analogy: A : B :: C : ? Figure A is rotated 90° clockwise to become Figure B. What should Figure '?' look like when the same rotation is applied to Figure C?
Step-by-Step Solution:

STEP 1: Identify the Transformation
- Figure A: Triangle in original orientation
- Figure B: Same triangle rotated 90° clockwise
- Transformation: 90° clockwise rotation

STEP 2: Apply to Figure C
- Figure C: Rectangle (horizontal orientation)
- After 90° clockwise rotation: Rectangle becomes vertical
- The shape remains a rectangle, only orientation changes

STEP 3: Verify
- Shape preserved ✓
- Size preserved ✓
- Only orientation changed by 90° clockwise ✓

Answer: Rectangle rotated 90° clockwise (becomes vertical)
rotation, orientation, basic-transformation

Question 4

Figure Analogy: A : B :: C : ? Figure A is rotated 90° anticlockwise to become Figure B. What should Figure '?' look like when the same rotation is applied to Figure C?
Step-by-Step Solution:

STEP 1: Identify the Transformation
- Figure A: Arrow in original orientation
- Figure B: Same arrow rotated 90° anticlockwise
- Transformation: 90° anticlockwise rotation

STEP 2: Apply to Figure C
- Figure C: Rectangle (horizontal orientation)
- After 90° anticlockwise rotation: Rectangle becomes vertical
- The shape remains a rectangle, only orientation changes

STEP 3: Verify
- Shape preserved ✓
- Size preserved ✓
- Only orientation changed by 90° anticlockwise ✓

Answer: Rectangle rotated 90° anticlockwise (becomes vertical)
rotation, orientation, basic-transformation

Question 5

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 6

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

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

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

Answer: Circle with 2 dots (1 more than original)
quantitative, progression, element-addition

Question 7

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 8

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 9

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 10

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 11

Figure Analogy: A : B :: C : ? Figure A is enlarged by 3× 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 square: 25 units
- Figure B square: 75 units
- Scaling factor = 75/25 = 3

STEP 2: Apply to Figure C
- Figure C: Circle
- Apply scaling factor 3
- New dimensions = original × 3

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

Answer: Circle enlarged by 3×
scaling, size-change, proportional

Question 12

Figure Analogy: A : B :: C : ? Figure A has 1 dot. Figure B has 3 dots (2 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 + 3 dots
- Change: +2 dots added

STEP 2: Apply to Figure C
- Figure C: Different container + 1 dot
- Add 2 more dots
- Result: Container + 3 dots total

Answer: Circle with 3 dots (1 original + 2 added)
element-count, addition, quantitative

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, all shaded regions become unshaded and vice versa (color inversion). Apply the same inversion to Figure C.
Step-by-Step Solution:

STEP 1: Identify Transformation
- A: Light background, dark internal elements
- B: Dark background, light internal elements
- Rule: Complete color/shading inversion

STEP 2: Apply to Figure C
- C: Light background, dark internal elements
- After inversion: Dark background, light internal elements
- All positions and shapes preserved

Answer: Circle with inverted shading
inversion, shading, color-swap

Question 15

Figure Analogy: A : B :: C : ? Figure A is rotated 180° to become Figure B. Apply the same 180° rotation to Figure C.
Step-by-Step Solution:

STEP 1: Identify Rotation Angle
- A and B: 180° rotation (half turn)
- Every point moves to opposite side

STEP 2: Apply to Figure C
- Rotate C 180° around its center
- Shape preserved, orientation inverted
- Dot moves to opposite position

Answer: Diamond rotated 180° (upside down) with dot repositioned
rotation, inversion, complex-orientation

Question 16

Figure Analogy: A : B :: C : ? Figure A has 1 dot. Figure B has 3 dots (2 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 + 3 dots
- Change: +2 dots added

STEP 2: Apply to Figure C
- Figure C: Different container + 1 dot
- Add 2 more dots
- Result: Container + 3 dots total

Answer: Circle with 3 dots (1 original + 2 added)
element-count, addition, quantitative

Question 17

Figure Analogy: A : B :: C : ? Figure A has 1 dot. Figure B has 3 dots (2 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 + 3 dots
- Change: +2 dots added

STEP 2: Apply to Figure C
- Figure C: Different container + 1 dot
- Add 2 more dots
- Result: Container + 3 dots total

Answer: Circle with 3 dots (1 original + 2 added)
element-count, addition, quantitative

Question 18

Figure Analogy: A : B :: C : ? In A→B, all shaded regions become unshaded and vice versa (color inversion). Apply the same inversion to Figure C.
Step-by-Step Solution:

STEP 1: Identify Transformation
- A: Light background, dark internal elements
- B: Dark background, light internal elements
- Rule: Complete color/shading inversion

STEP 2: Apply to Figure C
- C: Light background, dark internal elements
- After inversion: Dark background, light internal elements
- All positions and shapes preserved

Answer: Square with inverted shading
inversion, shading, color-swap

Question 19

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

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

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

Answer: Square with 3 dots (1 more than original)
quantitative, progression, element-addition

Question 20

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
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