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

Answer:

The correct option is A.

Step-by-step 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

$(x,y)\rightarrow (\frac{1}{2}x,\frac{1}{2}y)$

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

$B(-4,6)\rightarrow B'(\frac{1}{2}(-4),\frac{1}{2}(6))$

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

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