Question

triangle p has side lengths of 9, 12, and 15. triangle q is a dilation of triangle p with the center at the origin, and its hypotenuse is 5. the scale factor from triangle p to triangle q is

Explanation:

Step1: Recall the formula for scale factor

The scale factor \(k\) of a dilation is given by \(k=\frac{\text{length of a side in image}}{\text{length of the corresponding side in pre - image}}\)

Step2: Identify the corresponding sides

In triangle \(P\), the hypotenuse (longest side) is \(15\). In triangle \(Q\), the hypotenuse is \(5\)

Step3: Calculate the scale factor

Using the formula \(k=\frac{\text{hypotenuse of }Q}{\text{hypotenuse of }P}\), we substitute the values: \(k = \frac{5}{15}=\frac{1}{3}\)

Answer:

\(\frac{1}{3}\)