Question

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

Explanation:

Step1: Analyze each transformation type

• Reflection: Flips a figure over a line, but here the figures are similar in shape but different in size, not a flip.
• Rotation: Turns a figure around a point, doesn't change size proportionally like here.
• Translation: Slides a figure, doesn't change size, but here sizes changed.
• Dilation: Changes the size of a figure by a scale factor. Let's check the scale factor. For side \(QR = 4\) and \(Q'R' = 2\), scale factor is \(\frac{2}{4}=\frac{1}{2}\). For \(PQ = 2\) and \(P'Q' = 1\), scale factor is \(\frac{1}{2}\). For \(PS = 6\) and \(P'S' = 3\), scale factor is \(\frac{1}{2}\). So all sides are scaled by \(\frac{1}{2}\), which is dilation.

Answer:

dilation