The correct answer is:
C) k = 1/2
Step-by-step 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.