Question

Rectangle ABCD is dilated by a scale factor of 1/2 with a center of dilation at the origin. What are the coordinates of the image of point B'?

A. (–2, 3)
B. (3, –2)
C. (–8, 12)
D. (12, –8)

Answer 1

A. (-2,3) because Rectangle ABCD is dilated by a scale factor of 1/2.

Answer 2

The correct option is A.

Explanation:

If a figure dilated by a scale factor of k with a center of dilation at the origin, then

`(x,y)\rightarrow (kx,ky)`

It is given that rectangle ABCD is dilated by a scale factor of 1/2 with a center of dilation at the origin, so

`(x,y)\rightarrow ((1)/(2)x,(1)/(2)y)`

The coordinates of B are (-4,6). So, the coordinates of B' are

`B(-4,6)\rightarrow B'((1)/(2)(-4),(1)/(2)(6))`

`B(-4,6)\rightarrow B'(-2,3)`

The coordinates of B' are (-2,3), therefore option A is correct.