Question

triangle qrs is dilated by a scale factor of \\(\frac{1}{4}\\) to form triangle qrs. side rs measures 36. what is the measure of side rs?

Explanation:

Step1: Recall dilation property

When a figure is dilated by a scale factor \( k \), the length of its corresponding sides is multiplied by \( k \). Here, scale factor \( k=\frac{1}{4} \), and original side \( RS = 36 \).

Step2: Calculate length of \( R'S' \)

To find \( R'S' \), multiply \( RS \) by the scale factor. So, \( R'S'=RS\times\frac{1}{4} \). Substitute \( RS = 36 \) into the formula: \( R'S' = 36\times\frac{1}{4} \). Simplify the multiplication: \( 36\times\frac{1}{4}=\frac{36}{4} = 9 \).

Answer:

9