Question

The vertices of a parallelogram are shown below.

(0, 0), (27, 0), (36, 30), (9, 30)

Which of the following points is a vertex for the image produced by a dilation about the origin with a scale factor of 1/3?









A.

(3, 3)

B.

(10, 9)

C.

(3, 15)

D.

(3, 10)

Answer 1

The vertices for the dilated image can be found by multiplying the coordinates of the original image by the scale factor. In this problem, the scale factor is 1/3.

(0,0) ⇒ 0 x 1/3 = 0 ; 0 x 1/3 = 0 ⇒ (0,0)
(27,0) ⇒ 27 x 1/3 = 9 ; 0 x 1/3 = 0 ⇒ (9,0)
(36,30) ⇒36 x 1/3 = 12 ; 30 x 1/3 = 10 ⇒ (12,10)
(9,30) ⇒ 9 x 1/3 = 3 ; 30 x 1/3 = 10 ⇒ (3,10)

Answer is choice D. (3,10)