Answer:
Explanation:
To find the perimeter of triangle △PQR with vertices P(-9,2), Q(-7,3), and R(3,2), you can use the distance formula to calculate the lengths of its sides.
The distance formula for the distance between two points (x1, y1) and (x2, y2) is:
Distance = √((x2 - x1)^2 + (y2 - y1)^2)
Let's calculate the lengths of the three sides:
Length of side PQ:
Distance PQ = √((-7 - (-9))^2 + (3 - 2)^2)
Distance PQ = √(2^2 + 1^2)
Distance PQ = √(4 + 1)
Distance PQ = √5
Length of side QR:
Distance QR = √((3 - (-7))^2 + (2 - 3)^2)
Distance QR = √(10^2 + (-1)^2)
Distance QR = √(100 + 1)
Distance QR = √101
Length of side RP:
Distance RP = √((3 - (-9))^2 + (2 - 2)^2)
Distance RP = √(12^2 + 0^2)
Distance RP = √(144 + 0)
Distance RP = √144
Distance RP = 12
Now, you can find the perimeter by adding up the lengths of the three sides:
Perimeter = PQ + QR + RP
Perimeter = √5 + √101 + 12
So, the perimeter of triangle △PQR is √5 + √101 + 12 units.