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Your progress through Figure Analogy
Worksheet 23 of 30 (76% complete)
Question 1
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)
Question 2
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)
Question 3
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
Question 4
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
Question 5
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)
Question 6
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
Question 7
Figure Analogy: A : B :: C : ?
Rule: If a figure has more than 4 sides, add a central dot. Otherwise, keep unchanged. Apply to C.
STEP 2: Analyze Figure B (Result) - Shape: Pentagon (5-sided polygon - same as A) - Internal elements: One central dot added - Transformation applied: Dot added (condition met)
STEP 3: Extract Transformation Rule - Condition: Count number of sides - Decision point: Compare to 4 - If sides > 4: Add central dot - If sides ≤ 4: No change
STEP 4: Analyze Figure C Properties - Shape: Rectangle (4-sided polygon) - Sides count: 4 = 4 (NOT greater than 4) - Current internal elements: None
STEP 5: Apply Conditional Rule to C - Rectangle has 4 sides - Is 4 > 4? NO - Condition NOT met - Action: NO transformation (keep unchanged)
Answer: Rectangle remains completely unchanged (has exactly 4 sides, does not meet the "> 4" condition)
Question 8
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 circle: 20 units - Figure B circle: 60 units - Scaling factor = 60/20 = 3
STEP 2: Apply to Figure C - Figure C: Square - Apply scaling factor 3 - New dimensions = original × 3
STEP 3: Verify - Shape type preserved ✓ - Proportions preserved ✓ - Only size changed ✓
Answer: Square enlarged by 3×
Question 9
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×
Question 10
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 ✓
STEP 2: Analyze Figure B (Result) - Shape: Pentagon (5-sided polygon - same as A) - Internal elements: One central dot added - Transformation applied: Dot added (condition met)
STEP 3: Extract Transformation Rule - Condition: Count number of sides - Decision point: Compare to 4 - If sides > 4: Add central dot - If sides ≤ 4: No change
STEP 4: Analyze Figure C Properties - Shape: Rectangle (4-sided polygon) - Sides count: 4 = 4 (NOT greater than 4) - Current internal elements: None
STEP 5: Apply Conditional Rule to C - Rectangle has 4 sides - Is 4 > 4? NO - Condition NOT met - Action: NO transformation (keep unchanged)
Answer: Rectangle remains completely unchanged (has exactly 4 sides, does not meet the "> 4" condition)
Question 12
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
Question 13
Figure Analogy: A : B :: C : ?
Figure A is reduced to 0.5× original size 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: 12 units - Scaling factor = 12/25 = 0.5
STEP 2: Apply to Figure C - Figure C: Circle - Apply scaling factor 0.5 - New dimensions = original × 0.5
STEP 3: Verify - Shape type preserved ✓ - Proportions preserved ✓ - Only size changed ✓
Answer: Circle reduced to 0.5× original size
Question 14
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
Question 15
Figure Analogy: A : B :: C : ?
Rule: If a figure has more than 4 sides, add a central dot. Otherwise, keep unchanged. Apply to C.
STEP 2: Analyze Figure B (Result) - Shape: Pentagon (5-sided polygon - same as A) - Internal elements: One central dot added - Transformation applied: Dot added (condition met)
STEP 3: Extract Transformation Rule - Condition: Count number of sides - Decision point: Compare to 4 - If sides > 4: Add central dot - If sides ≤ 4: No change
STEP 4: Analyze Figure C Properties - Shape: Rectangle (4-sided polygon) - Sides count: 4 = 4 (NOT greater than 4) - Current internal elements: None
STEP 5: Apply Conditional Rule to C - Rectangle has 4 sides - Is 4 > 4? NO - Condition NOT met - Action: NO transformation (keep unchanged)
Answer: Rectangle remains completely unchanged (has exactly 4 sides, does not meet the "> 4" condition)
Question 16
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: L-shape in original orientation - Figure B: Same L-shape 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 ✓