Hakim is given a geometry task. On the left side of a vertical dashed line, his teacher has drawn the LEFT HALF of a figure. The left half shows a shape with: • A vertical left edge of 10 cm • A horizontal top edge of 5 cm • A right edge that meets the dashed line Hakim is told: "The dashed vertical line is a LINE OF SYMMETRY. Reflect the left half to complete the figure." After Hakim completes the full figure by reflecting the left half across the dashed line, how many lines of symmetry does the COMPLETE figure have?
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Worked Solution
Step 1: Complete the figure by reflection.
The left half has: a vertical left edge of 10 cm, a horizontal top edge of 5 cm meeting the dashed line, and a right edge of 10 cm along the dashed line. Reflecting this shape across the dashed vertical line produces a mirror image on the right side. The complete figure has: total width = 5 cm (left) + 5 cm (right) = 10 cm; height = 10 cm.
Step 2: Identify the complete figure.
A figure with all four sides equal (10 cm) and all four right angles is a SQUARE.
Step 3: Count the lines of symmetry of a square.
Line 1: Vertical line through the midpoints of the top and bottom sides.
Line 2: Horizontal line through the midpoints of the left and right sides.
Line 3: Diagonal from top-left corner to bottom-right corner.
Line 4: Diagonal from top-right corner to bottom-left corner.
Total: 4 lines of symmetry.
Answer: 4
Correct answer: 4
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