Question

Use a graph sheet for this question. Take 1 cm = 1 unit along both the x and y axis. Plot ABCDE, where A(4, 0), B(4, 2), C(2, 2), D(2, 4) and E(0, 4).

1. Reflect the points A, B, C and D on the y-axis and name them as F, G, H and I, respectively.
2. Join the points A, B, C, D, E, I, H, G and F in order. Reflect the figure ABCDEIHGF on the x-axis and name it as AMNPQRSTF.
3. Give the geometrical name of the closed figure AEFQ.

Answer 1

Steps of construction:

1. Plot the points: A(4, 0), B(4, 2), C(2, 2), D(2, 4) and E(0, 4).
2. By reflecting the points A, B, C and D on the y-axis, they become F, G, H and I, respectively.
3. Join the ABCDEIHGF points.
4. Reflect the figure ABCDEIHGF in the x-axis.
5. On reflecting the points A and F in the x-axis, they remain the same, as they lie on the x-axis.
6. When reflecting points B, C, D, E, I, H and G on the x-axis, they become M, N, P, Q, R, S and T, respectively.
7. Join the points A, E, F and Q.

In figure AEFQ,

There are four congruent isosceles right-angle triangles.

Thus, all the sides AE, EF, FQ and QA are equal.

Also, each interior angle is equal to 90°.

Hence, the figure AEFQ is square.