Question

the rectangle ( vwxy ) is a dilation of the rectangle ( vwxy ). 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 in the original rectangle

Take side \(VW\). \(V\) is at \((5,3)\) and \(W\) is at \((5,0)\). The length \(VW=\vert3 - 0\vert= 3\) units.

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

Take side \(V'W'\). \(V'\) is at \((2,1)\) and \(W'\) is at \((2,0)\). The length \(V'W'=\vert1 - 0\vert = 1\) unit.

Step3: Calculate the scale factor

The scale factor \(k=\frac{\text{length of side in dilated figure}}{\text{length of side in original figure}}\). So \(k=\frac{V'W'}{VW}=\frac{1}{3}\).

Answer:

$\frac{1}{3}$