Calculate the scale factor of the dilation around the center of dilation, c. the preimage is blue and the image is red.
a. k = 1/4
b. k = 1/3
c. k = 1/2
d. 2

The correct answer is:

C) k = 1/2

Explanation:

We will find the lengths of the horizontal segments of the pre-image and the image, and compare them to find the dilation factor.

For the pre-image, we have a horizontal segment from (2, 5) to (4, 5). This is a distance of 2.

The corresponding segment of the image goes from (2.5, 4) to (3.5, 4). This is a distance 1.

The segment of the image is 1/2 the size of the corresponding segment of the pre-image; this makes the dilation factor 1/2.

To verify, we have another horizontal segment of the pre-image that goes from (3, 2) to (6, 2). This is a distance of 3 units.

The corresponding horizontal segment of the image goes from (3, 2.5) to (4.5, 2.5). This is a distance of 1.5 units.

The distance of the image segment is 1/2 of the distance of the pre-image segment; this means the scale factor is 1/2.

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