Question

△qrs is the image of △qrs under a dilation through point c. what scale factor was used in the dilation? -4 -0.25 0.25 4

Explanation:

Step1: Recall dilation 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, i.e., $k=\frac{\text{length of side in image}}{\text{length of side in pre - image}}$.

Step2: Identify corresponding sides

Let's consider side $RS$ and $R'S'$. The length of $RS = 3$ cm and the length of $R'S'=12$ cm.

Step3: Calculate scale factor

$k=\frac{R'S'}{RS}=\frac{12}{3}=4$. Also, since the image and pre - image are in the same orientation (no indication of a flip), the scale factor is positive.

Answer:

4