Answered

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?

Verified Answer :

smmwaite

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 

JeanaShupp

Answer: 0.4

Step-by-step 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 :-

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

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

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