Question

Square ABCD is located on a coordinate plane. The coordinates for three of the vertices are listed below.

A (2,7) , C (8,1),D (2,1)
Square ABCD is dilated by a scale factor of 2 with the center of dilation at the origin, to form square A’B’C’D’. What are the coordinates if vertex B’?

Answer 1

B' has coordinates (16,14).

Step-by-step explanation

The given coordinates of square ABCD are :

A (2,7) , C (8,1),D (2,1)

In order to form a square, the coordinates of B should be: (8,7)

The mapping for dilation with a scale factor 2, about the origin is

`(x,y)\to (2x,2y)`

This implies that:

`B(8,7)\to B'(2 * 8,2 * 7)`

When we simplify we get:

`B(8,7)\to B'(16,14)`

Hence B' has coordinates (16,14).