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 scale - factor formula

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

Step2: Identify lengths

We are given that \(MP\) is the length of a side in the pre - image (\(MP = 10\)) and \(M'P'\) is the length of the corresponding side in the image (\(M'P'=4\)).

Step3: Calculate scale factor

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

Answer:

C. 0.4