Question

Select the correct answer.
Triangle E'F'G' is the image of triangle EFG after a dilation with center at (2-3).
What is the scale factor of this dilation?
A: 2
B: 3
C: 1/2
D: 1/3

Answer 1

Answer: D)  1/3

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Explanation:

Start at (2,-3). Move up 3 and over to the right 6 spots to move to (8,0) which is where point F is located.

We can write the slope as rise/run = 3/6

Go back to (2,-3). Move up 1 and to the right 2 spots to arrive at F ' (4,-2)

Let's now compare the upward movements:

• Initially we moved up 3 units when trying to get to point F
• Now we're only moving up 1 unit when getting to F'

The starting point each time is (2,-3) which is the center of dilation. The jump from 3 to 1 is "times 1/3" and that's our scale factor. Every linear distance in the image is 1/3 times as long compared to the preimage.

We can also get the same scale factor when comparing the horizontal movements as well. The jump from 6 to 2 is also "times 1/3".