Question

the rectangle wxyz is a dilation of the rectangle wxyz. 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 length of corresponding sides

Let's take side \(XY\) and \(X'Y'\).
Coordinates of \(X(8,8)\), \(Y(4,8)\), so length of \(XY=\vert8 - 4\vert=4\).
Coordinates of \(X'(2,2)\), \(Y'(1,2)\), so length of \(X'Y'=\vert2 - 1\vert = 1\).

Step2: Calculate scale factor

Scale factor \(k=\frac{\text{length of side in image}}{\text{length of side in original}}\).
\(k=\frac{X'Y'}{XY}=\frac{1}{4}\)

Answer:

\(\frac{1}{4}\)