Question

rectangle wxyz was dilated using the rule $d_{z,\frac{12}{5}}$. what is $wx$? 8 units 10 units 12 units 14 units

Explanation:

Step1: Recall the dilation formula

When a figure is dilated with a scale factor \(k\), the length of a side \(s'\) of the dilated figure is \(s'=k\times s\), where \(s\) is the length of the corresponding side of the original figure. Here, the scale factor \(k = \frac{12}{5}\) and the original length \(WX= 5\) (assuming the original rectangle \(WXYZ\) has \(WX = 5\) from the smaller rectangle part shown, maybe a mis - label in the problem, if we consider the side corresponding to \(W'X'\) in dilation. Another way: if we assume the original side (from the smaller rectangle) \(WX = 5\) (since in dilation, all sides of the rectangle are scaled by the same factor).

$$W'X'=\frac{12}{5}\times WX$$

Step2: Substitute the value of \(WX\)

If \(WX = 5\) (assuming the original side length before dilation for the side corresponding to \(W'X'\) is \(5\) units. Maybe a mis - representation in the problem's figure labelling, but using the scale factor formula).

$$W'X'=\frac{12}{5}\times5 = 12$$

Answer:

12 units