Question

A (1, 1), B (5, 1), C(4, 2) and D (2, 2) are vertices of a quadrilateral ABCD. A, B, C, and D are reflected in the origin on to A', B', C' and D' respectively. Locate A', B', C' and D' on the graph sheet and write their co-ordinates. Are D, A, A' and D' collinear ?

Answer 1

Choose the coordinate axes as shown in the graph paper. Take 1 cm = 1unit on both axes.

Plot the points A(1, 1), B(5, 1), C(4, 2) and D (2, 2) on the graph paper.
The quadrilateral ABCD is an isosceles trapezium.
Reflect the points A, B, C and D in the origin onto the points A′, B′, C′ and D′ respectively as shown in the graph paper.
The coordinates of these points are :
A′ (–1, –1), B′ (– 5, –1), C′ (– 4, –2) and D′ (–2, –2).
On joining the points D and D′, we find that the points A and A′ lie on it. Hence, the points D, A, A′ and D′ are collinear.