Question

the trapezoid ( klmn ) is a dilation of the trapezoid ( klmn ). 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 corresponding side in both trapezoids

For trapezoid \( KLMN \), let's consider the horizontal side \( KN \). The \( x -\)coordinate of \( K\) is \(-6\) and of \( N\) is \(-6\) (vertical line). The \( y -\)coordinate of \( K\) is \(-6\) and of \( N\) is \(3\). The length of \( KN=\vert3 - (-6)\vert = 9\).
For trapezoid \( K'L'M'N'\), consider the corresponding vertical side \( K'N'\). The \( y -\)coordinate of \( K'\) is \(-2\) and of \( N'\) is \(1\). The length of \( K'N'=\vert1-(-2)\vert = 3\).

Step2: Calculate the scale factor

The scale factor \(s\) of a dilation is given by the formula \(s=\frac{\text{length of side in image}}{\text{length of side in pre - image}}\).
Substituting the values: \(s = \frac{K'N'}{KN}\)
Since \(K'N' = 3\) and \(KN=9\), then \(s=\frac{3}{9}\)
Simplify the fraction \(\frac{3}{9}=\frac{1}{3}\)

Answer:

\(\frac{1}{3}\)