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? -2.5 -0.4 0.4 2.5

Explanation:

Step1: Recall the formula for scale factor

The scale factor \(k\) of a dilation is given by \(k=\frac{\text{length of image segment}}{\text{length of pre - image segment}}\).

Step2: Substitute the given values

We are given that the length of the pre - image segment \(MP = 10\) and the length of the image segment \(M'P'=4\).
Since the image is on the same side of the center of dilation as the pre - image (the direction is not reversed), the scale factor \(k=\frac{M'P'}{MP}\).
Substitute \(M'P' = 4\) and \(MP = 10\) into the formula: \(k=\frac{4}{10}=0.4\)

Answer:

0.4