Question

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

Explanation:

1. Rotation: A rotation turns a figure around a fixed - point. The shape and size remain the same, but the orientation changes.
2. Dilation: A dilation changes the size of a figure. Here, the side - lengths of trapezoid \(PQRS\) and \(P'Q'R'S'\) are in proportion (\(\frac{1}{2}\) for non - parallel sides and \(\frac{2}{4}=\frac{1}{2}\) for parallel sides), which is a characteristic of dilation.
3. Translation: A translation moves a figure without rotation or reflection. The orientation and shape remain the same, and it doesn't change the size.
4. Reflection: A reflection flips a figure over a line of reflection.

Since the size of trapezoid \(PQRS\) has changed to form trapezoid \(P'Q'R'S'\) with side - lengths in a fixed ratio, it is a dilation.

Answer:

dilation