What is the perimeter of PQR with vertices P(-2, 9) Q(7, -3) and R(-2, -3) in the coordinate plane?

Solution:

As evident from the problem statement

The points P(-2, 9) and R(-2, -3) have the same x-coordinate.

Similarly the points Q(7, -3) and R(-2, -3) have the same y coordinate.

Therefore the line PR is perpendicular to line RQ.

In other words PRQ is a triangle which is right angled at R.

Hence perimeter of the right angled triangle = PR + RQ + PQ

Distance(PR) = √(-2 -(-2))² + (9 - (-3))²) = √0 + 12² = √144 = 12

Distance(QR) = √(7 - (-2))² + (-3 - (-3))² = √9² + 0² = √9² + 0² = √81= 9

Distance(PQ) = √(-2 - 7)² + (9 - (-3))² = √(-9)² + (12)² = √81 + 144)² = √225 = 15

The perimeter of the the right angled triangle is:

Perimeter of ⊿PQR = 12 + 9 + 15 = 36

What is the perimeter of PQR with vertices P(-2, 9) Q(7, -3) and R(-2, -3) in the coordinate plane?

Summary:

The perimeter of PQR with vertices P(-2, 9) Q(7, -3) and R(-2, -3) in the coordinate plane is 36