Question

the rectangle ( rstu ) is a dilation of the rectangle ( rstu ). what is the scale factor of the dilation?
simplify your answer and write it as a proper fraction, an improper fraction, or a whole number.

Explanation:

Step1: Find the length of a side of the original rectangle

For rectangle \(RSTU\), let's consider the side \(ST\). The \(x -\)coordinates of \(S(3,1)\) and \(T(3, - 1)\). The length of \(ST=\vert1-(-1)\vert = 2\) units.

Step2: Find the length of the corresponding side of the dilated rectangle

For rectangle \(R'S'T'U'\), consider the side \(S'T'\). The \(x -\)coordinates of \(S'(9,3)\) and \(T'(9,-3)\). The length of \(S'T'=\vert3 - (- 3)\vert=6\) units.

Step3: Calculate the scale factor

The scale factor \(k\) of a dilation is given by \(k=\frac{\text{length of side in image}}{\text{length of side in pre - image}}\). So \(k = \frac{6}{2}=3\)

Answer:

\(3\)