Question

The smaller triangle is a pre-image of the bigger triangle. The center of dilation is (1, −1).

What is the scale factor used to create the dilation?

A 1/4
B 6
C -4
D 4

Answer 1

The answer is -4.

Explanation:

Answer 2

The scale factor is
`-4`

Explanation:

Lets have a look to the co-ordinates of triangle ABC and A'B'C.

The point of C=
`(1,-1)` and B=
`(-1,-1)`

The point of C=
`(1,-1)` and A'=
`(9,-1)`

By applying distance formula we can calculate the distance of line segment :
`√((x1-x)^2+(y1-y)^2)`

BC =
`√((1+1)^2+(0)^2)`=
`√(4)`=2

Similarly CA=
`√(64)`=8

Scale factor = K=
`(CA')/(BC)`=
`(8)/(2)`=4

The image and its preimage lies in opposite sides of center of dilation, C=
`(1,-1)` therefore the scale factor will be negative.

Our final answer = -4