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 each side is multiplied by \( k \). Here, scale factor \( k=\frac{1}{4} \) and original side \( RS = 36 \).

Step2: Calculate new side length

Multiply original length by scale factor: \( R'S'=RS\times\frac{1}{4}=36\times\frac{1}{4} \)
\( 36\times\frac{1}{4}=\frac{36}{4} = 9 \)

Answer:

9