Question

Rectangle WXYZ was dilated using the rule Rectangle W X Y Z is dilated to form rectangle W prime X prime Y prime Z prime. The length of W X is 5 and the length of X Y is 4..

D Subscript Z, twelve-fifths

What is W'X'?

8 units
10 units
12 units
14 units

Answer 1

To solve for the length of \( W'X' \) after dilation, we need to understand the dilation factor.

Given:
- The dimensions of rectangle \( WXYZ \) are \( WX = 5 \) (length) and \( XY = 4 \) (width).
- The length of side \( ZD \) is given as \( \frac{12}{5} \).

To find \( W'X' \), we first determine the dilation factor. Since \( ZD \) is an arbitrary value, we interpret it as the scale of the dilation from rectangle \( WXYZ \) to its dilated form \( W'X'Y'Z' \).

The dilation factor can be defined by the lengths:
\[
\text{Dilation factor} = \frac{W'X'}{WX}
\]
Let \( k \) be the dilation factor. Based on the problem context, if we know that \( W'X' \) is stretched by the same factor that \( ZD \) is stretched, we have:
\[
\frac{W'X'}{5} = \frac{12}{5}
\]
This means:
\[
W'X' = 5 \times \frac{12}{5} = 12
\]

Thus, the length of \( W'X' \) is **12 units**.

The answer is **12 units**.