Question

triangle pqr is reflected across side pr and then rotated 90° counterclockwise about point p to create image △pqr. move values to the lines to describe △pqr. the length of side pq is __ units, and the measure of angle q is __. 6 8 10 37° 53° 90°

Explanation:

Step1: Recall Transformations' Effect

Reflections and rotations are rigid transformations, so they preserve side lengths and angle measures. So, the length of \(P'Q'\) should equal the length of \(PQ\), and the measure of \(\angle Q'\) should equal the measure of \(\angle Q\).

Step2: Identify \(PQ\) Length

In \(\triangle PQR\), the length of \(PQ\) is given as 10. So, \(P'Q' = PQ = 10\) units.

Step3: Identify \(\angle Q\) Measure

In \(\triangle PQR\), the measure of \(\angle Q\) is given as \(53^\circ\). So, \(\angle Q'=\angle Q = 53^\circ\).

Answer:

10, \(53^\circ\)