Question

wxyz is a dilation image of wxyz. which is the correct description of the dilation?

an enlargement with scale factor 1/2
an enlargement with scale factor 2
a reduction with scale factor 2
a reduction with scale factor 1/2

Explanation:

Step1: Identify side lengths

First, find the side length of the original figure \( WXYZ \) and the dilated figure \( W'X'Y'Z' \). For \( WXYZ \), looking at the coordinates (or grid), the length from \( Z \) to \( X \) (or \( W \) to \( Z \)): from \( x = 2 \) to \( x = 6 \) (or \( y = 4 \) to \( y = 8 \))? Wait, actually, \( WXYZ \) is a square. Let's check the horizontal side: from \( W(2,8) \) to \( X(6,8) \), so length is \( 6 - 2 = 4 \). For \( W'X'Y'Z' \), \( W'(1,4) \) to \( X'(3,4) \), length is \( 3 - 1 = 2 \).

Step2: Calculate scale factor

Scale factor \( k=\frac{\text{length of image}}{\text{length of original}}=\frac{2}{4}=\frac{1}{2} \). Since the image is smaller than the original, it's a reduction with scale factor \( \frac{1}{2} \).

Answer:

a reduction with scale factor 1/2