Question

ΔRST is dilated about the origin, O, to create ΔR'S'T'. Point R is located at (3, 9), and point R' is located at (1.2, 3.6). Which scale factor was used to perform the dilation?

Answer 1

Answer: 0.4

Explanation:

We know that the a scale factor for dilation about the origin, O is the ratio of the coordinates of the image to the coordinates of the pre-image.

Given : ΔRST is dilated about the origin, O, to create ΔR'S'T'. Point R is located at (3, 9), and point R' is located at (1.2, 3.6).

Then , the scale factor for dilation is given by :-

`k=\frac{\text{x-coordinate of R'}}{\text{x-coordinate of R}}\\\\=(1.2)/(3)=0.4`

Therefore , the scale factor was used to perform the dilation= 0.4.

Answer 2

Answer
scale factor=0.4

Explanation
The scale factor for any transformation is the ration of the image distance to the object distance.
That is the ratio of distance from the origin to the image to the distance from the origin to the object.
In the case above, OR’is the image distance and OR is the object distance.
OR’ = √(〖1.2〗^2+〖3.6〗^2 )=√14.4=3.794733192
OR = √(3^2+9^2 )=√90=9.486832981

The scale factor = 3.794733192/9.486832981
=0.4