What is the perimeter of trianglePQR with vertices P(–2, 9), Q(7, –3), and R(–2, –3) in the coordinate plane?
(1 point)
Responses
21 units
21 units
25 units
25 units
34 units
34 units
36 units
To find the perimeter of the triangle, we need to calculate the length of each side and then add them together.
First, we find the length of side PQ:
PQ = √((x₂ - x₁)² + (y₂ - y₁)²)
= √((7 - (-2))² + (-3 - 9)²)
= √((7 + 2)² + (-12)²)
= √(9² + 144)
= √(81 + 144)
= √225
= 15
Next, we find the length of side QR:
QR = √((x₂ - x₁)² + (y₂ - y₁)²)
= √((-2 - 7)² + (-3 - (-3))²)
= √((-9)² + 0²)
= √(81 + 0)
= √81
= 9
Finally, we find the length of side RP:
RP = √((x₂ - x₁)² + (y₂ - y₁)²)
= √((-2 - (-2))² + (-3 - 9)²)
= √((0)² + (-12)²)
= √(0 + 144)
= √144
= 12
Now, we can add the lengths of the sides to find the perimeter:
Perimeter = PQ + QR + RP
= 15 + 9 + 12
= 36
Therefore, the perimeter of triangle PQR is 36 units.
To find the perimeter of triangle PQR, we need to calculate the distance between each pair of vertices.
1. Distance between P(-2, 9) and Q(7, -3):
- Using the distance formula: d = √((x2 - x1)^2 + (y2 - y1)^2)
- d = √((7 - (-2))^2 + (-3 - 9)^2)
- d = √((9)^2 + (-12)^2)
- d = √(81 + 144)
- d = √225
- d = 15 units
2. Distance between Q(7, -3) and R(-2, -3):
- Using the distance formula: d = √((x2 - x1)^2 + (y2 - y1)^2)
- d = √((-2 - 7)^2 + (-3 - (-3))^2)
- d = √((-9)^2 + (0)^2)
- d = √(81 + 0)
- d = √81
- d = 9 units
3. Distance between R(-2, -3) and P(-2, 9):
- Using the distance formula: d = √((x2 - x1)^2 + (y2 - y1)^2)
- d = √((-2 - (-2))^2 + (9 - (-3))^2)
- d = √((0)^2 + (12)^2)
- d = √(0 + 144)
- d = √144
- d = 12 units
Now, we can calculate the perimeter by adding the distances:
Perimeter = 15 units + 9 units + 12 units
Perimeter = 36 units
Therefore, the perimeter of triangle PQR is 36 units.