Question

ABC is a triangle as shown in the figure below.

1. Write down the coordinates of A, B and C on reflecting through the origin. 
2. Write down the coordinates of the point/s which remain invariant on reflecting the triangle ABC on the x-axis and y-axis respectively.

Answer 1

Given: From the diagram, the vertices are A(4, 4), B(0, 3), C(3, 0).

a. Reflection of  A, B, C through the origin.

Reflection in the origin maps (x, y) to (–x, –y).

A(4, 4) to A’(–4, –4)

B(0, 3) to B’(0, –3)

C(3, 0) to C’(–3, 0)

b. Point(s) invariant under reflection in x-axis and y-axis respectively.

A point is invariant under reflection in the x-axis if it lies on the x-axis, i.e. y = 0.

Among A(4, 4), B(0, 3), C(3, 0), only (C) has y = 0.

So, (C) is invariant in x-axis.

A point is invariant under reflection in the y-axis if it lies on the y-axis, i.e. x = 0.

Among A(4, 4), B(0, 3), C(3, 0), only (B) has x = 0. 

So (B) is invariant in y-axis.

Invariant on reflection in x-axis: C(3, 0)

Invariant on reflection in y-axis: B(0, 3)