On square grid paper, Aisha draws the LEFT half of a symmetric figure as shown in the diagram. The dashed vertical line is the line of symmetry. The left half is a right-angled triangle whose vertical leg (4 cm) sits on the line of symmetry, with the horizontal leg (3 cm) extending to the LEFT and a slanting hypotenuse joining them. Which transformation of the left half correctly completes the symmetric figure on the right side of the line of symmetry?
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Worked Solution
Step 1: Recall what reflection across a vertical line of symmetry does. Every point on the left half has a matching 'mirror point' on the right half, the SAME distance from the line of symmetry, at the SAME height.
Step 2: Identify the three corners of the left-half triangle. Top corner: on the line of symmetry, 4 cm up. Bottom corner on the line: at the line, 0 cm up. Far corner: 3 cm LEFT of the line, 0 cm up.
Step 3: Reflect each corner across the vertical line of symmetry. The two corners on the line stay put. The corner that is 3 cm LEFT of the line moves to 3 cm RIGHT of the line, at the same height.
Step 4: Connect the reflected corners. The right half is a right-angled triangle with vertical leg 4 cm on the line, horizontal leg 3 cm extending to the RIGHT, and a slanting hypotenuse — i.e. a REFLECTION of the left half.
Step 5: Check: left + right halves together form an isosceles triangle with base 6 cm and height 4 cm. ✓
Final answer: Reflection (3 cm horizontal leg pointing right).
Answer: Reflection (3 cm horizontal leg pointing right)
Correct answer: Reflection (3 cm horizontal leg pointing right)
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