Question

triangle rst was dilated by a scale factor of $\frac{1}{2}$. the image, triangle rst, is an isosceles triangle, with each leg measuring 8 units. what is the length of a leg of the pre - image, triangle rst? 4 units 8 units 16 units 20 units

Explanation:

Step1: Recall the dilation formula

When a figure is dilated, the formula is \( \text{Image length}=\text{Scale factor}\times\text{Pre - image length}\). Let \(x\) be the length of a leg of the pre - image. We know that the scale factor \(k = \frac{1}{2}\) and the image length \(y=8\) units.

Step2: Solve for the pre - image length

Using the formula \(y = kx\), we substitute \(y = 8\) and \(k=\frac{1}{2}\). Then \(8=\frac{1}{2}x\). To solve for \(x\), we multiply both sides of the equation by \(2\). So \(x=8\times2\).

Answer:

\(16\) units (the third option)