Question

A quadrilateral with vertices at A(4, –4), B(4, –16), C(12, –16), and D(12, –4) has been dilated with a center at the origin. The image of D, point D, has coordinates (36, –12). What is the scale factor of the dilation?
1/9
1/3
3
9

Answer 1

Answer:

Scale factor of the dilation is 3            

Step-by-step explanation:

Given a quadrilateral with vertices at A(4, -4), B(4, -16), C(12, -16), and D(12, -4) has been dilated with a center at the origin. The image of D i.e coordinates of D after dilation are (36,-12).

we have to find the scale factor of the dilation.

As we know if the scale factor for dilation is k the new coordinates after dilation can be calculated as

(x,y) → (kx,ky)

As image of D given i.e

D(12,-4) → D'(36,-12)

⇒ 12 → 12k i.e 12k=36 ⇒ k=3

and -4 → -4k i.e -4k=-12 ⇒ k=3

hence, scale factor of the dilation is 3

Answer 2

I think the answer is 3, because D(12;-4) and D' is (36;-12). Then 36/12=3, -12/-4=3
(I hope it's true)!!! :)