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? \\(\bigcirc\\) 4 units \\(\bigcirc\\) 8 units \\(\bigcirc\\) 16 units \\(\bigcirc\\) 20 units

Explanation:

Step1: Recall Dilation Formula

Dilation scales a figure by a factor \( k \). If the image length is \( L' \) and pre - image length is \( L \), then \( L'=k\times L \). Here, \( k = \frac{1}{2} \) and \( L' = 8 \) units.

Step2: Solve for Pre - image Length

We need to find \( L \). From \( L'=k\times L \), we can re - arrange to \( L=\frac{L'}{k} \). Substitute \( L' = 8 \) and \( k=\frac{1}{2} \) into the formula. So \( L=\frac{8}{\frac{1}{2}}=8\times2 = 16 \) units.

Answer:

16 units (corresponding to the option "16 units")