Question

triangle qpr was dilated using the dilation rule o_{3,4}. what is pr? 6 units 9 units 12 units 18 units

Explanation:

Step1: Determine the scale factor

From the figure, assume \(PQ = 3\) units. After dilation, \(P'Q'= 9\) units. The scale factor \(k=\frac{P'Q'}{PQ}=\frac{9}{3} = 3\).

Step2: Calculate \(PP'\)

Let \(OP=x\). Then \(OP'=3x\). And \(PP'=OP' - OP=3x - x = 2x\). Also, since \(PQ = 3\) and \(P'Q' = 9\), we know that if we consider the distance from the center of dilation \(O\) (assume \(O\) is a common point in dilation). If \(PQ\) and \(P'Q'\) are corresponding sides, and using the property of dilation \(PP'=(3 - 1)\times6=12\) (assuming \(OQ = 6\) from the ratio relationship. Another way: If the scale factor \(k = 3\), and assume \(OP = 6\) (by observing the ratio of side lengths in similar triangles formed by dilation), then \(OP'=3\times6=18\), and \(PP'=OP' - OP=18 - 6=12\).

Answer:

12 units