What is the perimeter of PQR with vertices P(–2, 9), Q(7, –3), and R(–2, –3) in the coordinate plane?
To find the perimeter of a triangle, you need to calculate the sum of the lengths of all three sides.
To find the length of each side, you can use the distance formula, which is:
d = √((x2 - x1)^2 + (y2 - y1)^2)
Let's calculate the length of each side:
Side PQ:
P(–2, 9) and Q(7, –3)
d(PQ) = √((7 - (-2))^2 + (-3 - 9)^2)
= √((7 + 2)^2 + (-3 - 9)^2)
= √(9^2 + (-12)^2)
= √(81 + 144)
= √225
= 15
Side QR:
Q(7, –3) and R(–2, –3)
d(QR) = √((-2 - 7)^2 + (-3 - (-3))^2)
= √((-2 - 7)^2 + (-3 + 3)^2)
= √((-9)^2 + 0^2)
= √(81 + 0)
= √81
= 9
Side RP:
R(–2, –3) and P(–2, 9)
d(RP) = √((-2 - (-2))^2 + (9 - (-3))^2)
= √((-2 + 2)^2 + (9 + 3)^2)
= √(0^2 + 12^2)
= √(0 + 144)
= √144
= 12
Now, let's calculate the perimeter:
Perimeter = PQ + QR + RP
= 15 + 9 + 12
= 36
Therefore, the perimeter of triangle PQR is 36 units.
Use your distance between 2 points formula to find the 3 sides, then add them up
I will do one of them
PQ = √( 7-(-2))^2 + (-3-9)^2 )
= √(81 + 144) = √225 = 15