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?

Explanation:

Step1: Recall the definition of scale factor in dilation

The scale factor of a dilation is the ratio of the length of a side in the image to the length of the corresponding side in the original figure.
So, the scale factor \( k=\frac{\text{Length of side in image}}{\text{Length of corresponding side in original}} \)

Step2: Identify the corresponding sides

Here, \( M'P' \) is the side in the image \( \triangle M'N'P' \) and \( MP \) is the corresponding side in the original \( \triangle MNP \). We know \( MP = 10 \) and \( M'P'=4 \)

Step3: Calculate the scale factor

Substitute the values into the formula: \( k=\frac{M'P'}{MP}=\frac{4}{10}=\frac{2}{5} \)

Answer:

\(\frac{2}{5}\)