Question

15 square rstu is dilated to create square rstu using the origin as the center of dilation. which one of the following statements is true? a square rstu is dilated by a scale factor of 1/5 to create square rstu. b square rstu is dilated by a scale factor of 5 to create square rstu. c square rstu is dilated by a scale factor of 1/2 to create square rstu. d square rstu is dilated by a scale factor of 2 to create square rstu. 8.3c

Explanation:

Step1: Observe side - length comparison

Count the side - length of square RSTU and R'S'T'U'. Let's assume the side - length of square RSTU is \(a\) and that of R'S'T'U' is \(b\). By counting the grid units, if the side - length of square RSTU is 3 units and the side - length of square R'S'T'U' is 6 units.

Step2: Calculate scale factor

The scale factor \(k\) of dilation is given by the formula \(k=\frac{\text{side - length of image}}{\text{side - length of pre - image}}\). So \(k = \frac{b}{a}\). Substituting \(b = 6\) and \(a=3\), we get \(k = 2\).

Answer:

D. Square RSTU is dilated by a scale factor of 2 to create square R'S'T'U'