Question

What is the perimeter of triangle PQR with verticies P(-2,9), Q(7,-13), and R(-2,-3) in the coordinate plane

Answer 1

To find the perimeter of triangle PQR, we need to find the lengths of each side.

Using the distance formula, we can find the distance between points P and Q:
d(PQ) = sqrt((x2 - x1)^2 + (y2 - y1)^2)
= sqrt((7 - (-2))^2 + (-13 - 9)^2)
= sqrt(9^2 + (-22)^2)
= sqrt(81 + 484)
= sqrt(565)

Using the distance formula, we can find the distance between points Q and R:
d(QR) = sqrt((x2 - x1)^2 + (y2 - y1)^2)
= sqrt((-2 - 7)^2 + (-3 - (-13))^2)
= sqrt((-9)^2 + (10)^2)
= sqrt(81 + 100)
= sqrt(181)

Using the distance formula, we can find the distance between points R and P:
d(RP) = sqrt((x2 - x1)^2 + (y2 - y1)^2)
= sqrt((-2 - (-2))^2 + (-3 - 9)^2)
= sqrt(0^2 + (-12)^2)
= sqrt(0 + 144)
= sqrt(144)
= 12

Now, we can find the perimeter:
Perimeter = PQ + QR + RP
= sqrt(565) + sqrt(181) + 12

Therefore, the perimeter of triangle PQR is sqrt(565) + sqrt(181) + 12.