Question

△rst is the image of △rst under a dilation through point c. rs = 5 and rs = 8. what scale factor was used in the dilation? -1.6 -0.625 0.625 1.6

Explanation:

Step1: Recall scale - factor 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 values

We are given that the length of side \(RS\) in the pre - image \(\triangle RST\) is \(RS = 5\), and the length of the corresponding side \(R'S'\) in the image \(\triangle R'S'T'\) is \(R'S'=8\).

Step3: Calculate scale factor

Substitute the values into the formula: \(k=\frac{R'S'}{RS}=\frac{8}{5}=1.6\).

Answer:

E. 1.6