Question

the square ( tuvw ) is a dilation of the square ( tuvw ). what is the scale factor of the dilation?

Explanation:

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

The original square \( TUVW \). The \( y \)-coordinate of \( T \) is \( 2 \) and of \( U \) is \( 0 \). So the length \( TU=\vert2 - 0\vert=2 \).

Step2: Find the length of a side of the dilated square

The dilated square \( T'U'V'W' \). The \( y \)-coordinate of \( T' \) is \( 10 \) and of \( U' \) is \( 0 \). So the length \( T'U'=\vert10 - 0\vert = 10 \).

Step3: Calculate the scale factor

The scale factor \( k\) of a dilation is given by \(k=\frac{\text{length of side of dilated figure}}{\text{length of side of original figure}}\). So \(k=\frac{T'U'}{TU}=\frac{10}{2}=5\).

Answer:

The scale factor of the dilation is \(5\).