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

Step2: Solve for pre - image length

We know \( l = 8 \) and \( k=\frac{1}{2} \), substitute into the formula \( l = k\times L \), we get \( 8=\frac{1}{2}\times L \)
To solve for \( L \), multiply both sides of the equation by 2: \( L=8\times2 = 16 \)

Answer:

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