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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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