# 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

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