Question

What is the scale factor of this dilation? Line segments X Y and X prime Y prime. From the point of dilation, the distance to point Y is 3 and the distance to point X is 2. The distance from point Y to Y prime is 6, and the distance from X to X prime is 4.

A) One-half
B) One-third
C) 2
D) 3

Answer 1

The scale factor of the dilation described in the question is 2. This was determined by comparing the ratios of the distances from the original points to their images with those from the point of dilation to the original points, which both resulted in a scale factor of 2.

Step-by-step explanation:

The question involves finding the scale factor of a dilation using the distances from the original points to their images. We have two given line segments XY and X'Y', along with the distances from the points of dilation to both the original points and their dilated images. To find the scale factor, we need to compare the ratios of the distances from the original points to their images with the distances from the point of dilation to the original points.

For point Y, the dilation takes it from a distance of 3 units from the center to 6 units, and for point X, it moves from 2 units to 4 units.

Now, let's calculate the scale factor using the proportion for Y and X respectively:

• Scale Factor for Y = Distance to Y'/Distance to Y = 6/3
• Scale Factor for X = Distance to X'/Distance to X = 4/2

Both proportions result in a scale factor of 2.