Question

The smaller triangle is a pre-image of the bigger triangle. The center of dilation is (2, −2).

What is the scale factor used to create the dilation?




3

​ 13 ​

​−13 ​

−3

Answer 1

Answer: The correct option is fourth option, i.e., -3.

Step-by-step explanation:

It is given that the smaller triangle is a preimage of the bigger triangle. The center of dilation is (2, −2).

From the given figure it is noticed that the vertices of preimage are A(2,-2), B(2,2), C(-2,-2) and the vertices of preimage are A'(2,-2), B'(2,-14) and C'(14,-2).

The length of AB is 4 and the length of A'B' is 12.

The sides of image and preimage are in proportion.

proportion =
`(12)/(4) =3`

Since the image is enlargement of preimage therefore k>1 and k<-1.

Since the image and preimage are lies in opposite sides of center of dilation, therefore the scale factor must be negative.

`k=-3`

There correct option is option 4.