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).
(a) Reflect the points A, B, C and D on the y-axis and name them as F, G, H and I respectively.
(b) 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.
(c) Give the geometrical name of the closed figure AEFQ.
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Steps of Construction:
Plot the points : A(4, 0), B(4, 2), C(2, 2), D(2,4) and E(0, 4).
On reflecting the points A, B, C and D on the y-axis, they become F, G, H and I respectively.
Join the points ABCDEIHGF.
Reflect the figure ABCDEIHGF in x-axis.
On reflecting the points A and F in x-axis, they remain same as they lie on x-axis.
On 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.
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.