Question

The vertices of a trapezoid are shown below.

(0 , 6), (6 , 12), (6 , 9), (0 , 12)

Which of the following points is a vertex for the image produced by a dilation about the origin with a scale factor of 1/2 ?
A.
(2 , 14)

B.
(3 , 4.5)

C.
(6 , 3)

D.
(0 , 12)

Answer 1

Dilating about the origin by 1/2 sends (x,y) to (x/2, y/2). The vertices map to:
(0,6) -> (0,3)
(6,12) -> (3,6)
(6,9) -> (3,4.5)
(0,12) -> (0,6)

So the image includes (3,4.5), choice B.