What is the perimeter of triangle PQR with verticies P(-2,9), Q(7,-13), and R(-2,-3) in the coordinate plane
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.
To find the perimeter of a triangle, you need to calculate the sum of the lengths of its three sides.
Let's label the vertices P(-2,9), Q(7,-13), and R(-2,-3).
To find the length of a side, you can use the distance formula, which is:
Distance = √((x2 - x1)^2 + (y2 - y1)^2)
Now, let's calculate the length of each side:
1. Length of side PQ:
P(-2,9) and Q(7,-13)
Distance(PQ) = √((7 - (-2))^2 + (-13 - 9)^2)
= √(9^2 + (-22)^2)
= √(81 + 484)
= √565
≈ 23.78
2. Length of side QR:
Q(7,-13) and R(-2,-3)
Distance(QR) = √((-2 - 7)^2 + (-3 - (-13))^2)
= √((-9)^2 + 10^2)
= √(81 + 100)
= √181
≈ 13.45
3. Length of side RP:
R(-2,-3) and P(-2,9)
Distance(RP) = √((-2 - (-2))^2 + (9 - (-3))^2)
= √(0^2 + 12^2)
= √(0 + 144)
= √144
= 12
Finally, to find the perimeter, you sum up the lengths of all sides:
Perimeter = PQ + QR + RP
≈ 23.78 + 13.45 + 12
≈ 49.23
Therefore, the perimeter of triangle PQR is approximately 49.23 units.