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 the side lengths' ratios here don't suggest reflection.
• Rotation: Turns a figure around a point, but the proportional change in side lengths (e.g., \( \frac{1}{2},\frac{2}{4},\frac{1}{2},\frac{3}{6} \) all equal \( \frac{1}{2} \)) isn't rotation - related.
• Translation: Slides a figure without changing size/shape, but here the size changes (e.g., \( PQ = 2 \) in original, \( P'Q' = 1 \) in image), so not translation.
• Dilation: Scales a figure by a scale factor. Calculate the scale factor for corresponding sides: \( \frac{P'Q'}{PQ}=\frac{1}{2},\frac{Q'R'}{QR}=\frac{2}{4}=\frac{1}{2},\frac{R'S'}{RS}=\frac{1}{2},\frac{P'S'}{PS}=\frac{3}{6}=\frac{1}{2} \). All ratios are equal (\( \frac{1}{2} \)), so it's dilation.

Answer:

dilation