Question

determining the type of transformation
which type of transformation maps trapezoid pqrs onto trapezoid pqrs?
reflection
rotation
translation
dilation

Explanation:

Step1: Check side - length ratios

The side - lengths of trapezoid \(PQRS\) are \(PQ = 2\), \(QR=4\), \(RS = 2\), \(PS = 6\). The side - lengths of trapezoid \(P'Q'R'S'\) are \(P'Q'=1\), \(Q'R' = 2\), \(R'S'=1\), \(P'S'=3\). The ratio of corresponding side - lengths is \(\frac{P'Q'}{PQ}=\frac{1}{2}\), \(\frac{Q'R'}{QR}=\frac{2}{4}=\frac{1}{2}\), \(\frac{R'S'}{RS}=\frac{1}{2}\), \(\frac{P'S'}{PS}=\frac{3}{6}=\frac{1}{2}\).

Step2: Recall transformation definitions

A dilation is a transformation that changes the size of a figure, but not its shape. Since the shape of the trapezoid is the same and the side - lengths are in a constant ratio, it is a dilation.

Answer:

dilation