Question

1. which statement accurately describes the dilation of quadrilateral pqrs? select all that apply. a. the coordinates of quadrilateral pqrs are half of the coordinates of quadrilateral wxyz. b. the coordinates of quadrilateral pqrs are twice the coordinates of quadrilateral wxyz. c. the dilation is an enlargement. d. the dilation is a reduction. e. quadrilateral pqrs is dilated by a scale factor of 2. f. quadrilateral pqrs is dilated by a scale factor of $\frac{1}{2}$.

Explanation:

Step1: Analyze dilation concept

Dilation is a transformation that changes the size of a figure. If the scale - factor \(k> 1\), it is an enlargement; if \(0 < k<1\), it is a reduction.

Step2: Compare side - lengths or coordinates

By observing the figure, we can see that quadrilateral \(PQRS\) is smaller than quadrilateral \(WXYZ\). The coordinates of the vertices of \(PQRS\) are half of the coordinates of the vertices of \(WXYZ\). This means the scale factor \(k=\frac{1}{2}\). A scale factor of \(\frac{1}{2}\) indicates a reduction.

Answer:

A. The coordinates of quadrilateral \(PQRS\) are half of the coordinates of quadrilateral \(WXYZ\).
D. The dilation is a reduction.
F. Quadrilateral \(PQRS\) is dilated by a scale factor of \(\frac{1}{2}\).