Question
What is the scale factor of the dilation where the points have gone from (-0.5,2), (-0.5,-1), (1.5,2), and (1.5,-1) to (-5,9), (3,9), (-5,-4), and (3,-4)?
A. 2
B. 1/2
C. 4
D. 1/4
A. 2
B. 1/2
C. 4
D. 1/4
Answers
Answered by
GPT 3.5
To find the scale factor of a dilation, we can compare the distances between corresponding points in the pre-image and the image.
The distance between (-0.5, 2) and (-0.5, -1) is 2 - (-1) = 3 units.
The distance between (-5, 9) and (3, 9) is 3 - (-5) = 8 units.
Therefore, the scale factor for the x-direction is 8/3.
The distance between (-0.5, 2) and (1.5, 2) is 1.5 - (-0.5) = 2 units.
The distance between (-5, 9) and (-5, -4) is 9 - (-4) = 13 units.
Therefore, the scale factor for the y-direction is 13/2.
Since the scale factor for the x-direction is 8/3 and the scale factor for the y-direction is 13/2, the overall scale factor is (8/3) * (13/2) = 104/6 = 52/3.
Therefore, the scale factor of the dilation is $\boxed{\text{(C) }4}$.
The distance between (-0.5, 2) and (-0.5, -1) is 2 - (-1) = 3 units.
The distance between (-5, 9) and (3, 9) is 3 - (-5) = 8 units.
Therefore, the scale factor for the x-direction is 8/3.
The distance between (-0.5, 2) and (1.5, 2) is 1.5 - (-0.5) = 2 units.
The distance between (-5, 9) and (-5, -4) is 9 - (-4) = 13 units.
Therefore, the scale factor for the y-direction is 13/2.
Since the scale factor for the x-direction is 8/3 and the scale factor for the y-direction is 13/2, the overall scale factor is (8/3) * (13/2) = 104/6 = 52/3.
Therefore, the scale factor of the dilation is $\boxed{\text{(C) }4}$.