Question

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

Explanation:

Step1: Recall the scale factor formula for dilation

The scale factor \( k \) of a dilation is given by the ratio of the length of a side in the image (\( M'P' \)) to the length of the corresponding side in the original figure (\( MP \)). So the formula is \( k=\frac{\text{Length of image side}}{\text{Length of original side}} \).

Step2: Substitute the given values

We know that \( MP = 10 \) (original length) and \( M'P'=4 \) (image length). Substituting these values into the formula, we get \( k = \frac{M'P'}{MP}=\frac{4}{10} \).

Step3: Simplify the fraction

Simplifying \( \frac{4}{10} \), we divide both the numerator and the denominator by their greatest common divisor, which is 2. So \( \frac{4\div2}{10\div2}=\frac{2}{5} = 0.4 \).

Answer:

\( 0.4 \)