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 20 units 8 units 16 units

Explanation:

Step1: Recall dilation formula

Dilation: \( \text{Image length} = \text{Scale factor} \times \text{Pre - image length} \)
Let \( L \) be the length of the leg of pre - image \( \triangle RST \), and \( L' \) be the length of the leg of image \( \triangle R'S'T' \), scale factor \( k=\frac{1}{2} \), \( L' = 8 \) units.

Step2: Solve for pre - image length

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

Answer:

16 units