Question

△mnp is the image of △mnp under a dilation through point c. mp = 10 and mp = 4. what scale factor was used in the dilation? 0.4 2.5 -0.4 -2.5

Explanation:

Step1: Recall scale - factor formula

The scale factor $k$ of a dilation is given by the ratio of the length of a side of the image to the length of the corresponding side of the pre - image. That is $k=\frac{\text{length of side in image}}{\text{length of corresponding side in pre - image}}$.

Step2: Identify the lengths

We are given that $MP$ is a side of the pre - image with $MP = 10$ and $M'P'$ is the corresponding side of the image with $M'P'=4$.

Step3: Calculate the scale factor

Substitute the values into the formula: $k=\frac{M'P'}{MP}=\frac{4}{10}=0.4$.

Answer:

A. 0.4