Question

the trapezoid nopq is a dilation of the trapezoid nopq. 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: Identify corresponding sides

We can use the vertical sides \(PN\) and \(P'N'\) to find the scale factor.
Coordinates of \(P(-3,1)\) and \(N(3,3)\), so the length of \(PN=\vert3 - 1\vert= 2\) (using the distance formula for vertical lines \(d=\vert y_2 - y_1\vert\)).
Coordinates of \(P'(-8,3)\) and \(N'(9,9)\), so the length of \(P'N'=\vert9 - 3\vert=6\)

Step2: Calculate the scale factor

The scale factor \(k\) of a dilation is given by the formula \(k=\frac{\text{length of image side}}{\text{length of pre - image side}}\)
\(k=\frac{P'N'}{PN}\)
Substitute \(P'N' = 6\) and \(PN = 2\) into the formula: \(k=\frac{6}{2}=3\)

Answer:

\(3\)