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) 4
B) - 4
C) 6
D) 1/4

Answer 1

Answer: B) -4

Explanation:

Answer 2

B)-4

Explanation:

We are given that in a figure

The vertices of small triangle are (1,1),(-1,-1) and (1,-1).

The vertices of big triangle are (1,-9) ,(9,-1) and (1,-1).

Side of small triangle=
`√((-1-1)^2+(-1-1)^2)=2` units

By using the distance formula

Distance formula:
`√((x_2-x_1)^2+(y_2-y_1)^2)`

Side of big triangle =
`√((1-1)^2+(-1+9)^2)=8` units

From given figure we can see that the pre-image is rotated about 180 degree and then we get big triangle.Therefore, the scale factor is negative.

Scale factor=
`-(side\;of\;triangle)/(side\;of\;small\;triangle)`

By using the formula

Scale factor=
`-(8)/(2)=-4`

Hence, the scale factor used to create the dilation=-4