What is the perimeter of △PQR
with vertices P(-9,2), Q(-7,3) and R(3,2) . Round your answer to the nearest tenth. (1 point)
Responses
24.2 units
24.2 units
19.8 units
19.8 units
27.6 units
27.6 units
5.6 units
whats the answer
To find the perimeter of a triangle, we need to calculate the distance between each pair of vertices and then sum them up.
Using the distance formula √((x2-x1)^2 + (y2-y1)^2), we can find the distances:
Distance PQ = √((-7-(-9))^2 + (3-2)^2) = √(2^2 + 1^2) = √(4 + 1) = √5 ≈ 2.24 units
Distance QR = √((3-(-7))^2 + (2-3)^2) = √(10^2 + 1^2) = √(100 + 1) = √101 ≈ 10.05 units
Distance RP = √((-9-3)^2 + (2-2)^2) = √((-12)^2 + 0^2) = √(144 + 0) = √144 = 12 units
Now, we can sum up the distances:
Perimeter = PQ + QR + RP = 2.24 + 10.05 + 12 ≈ 24.29
Rounding to the nearest tenth, the perimeter of triangle PQR is approximately 24.3 units.
None of the given answer choices are correct, but the closest one is 24.2 units.
To find the perimeter of △PQR, we need to calculate the length of each side and then sum them up.
The distance between points P(-9,2) and Q(-7,3) can be calculated using the distance formula:
d(PQ) = √[(x₂ - x₁)² + (y₂ - y₁)²]
d(PQ) = √[(-7 - (-9))² + (3 - 2)²]
d(PQ) = √[2² + 1²]
d(PQ) = √[4 + 1]
d(PQ) = √5 ≈ 2.24 units (rounded to the nearest tenth)
The distance between points Q(-7,3) and R(3,2) can be calculated in the same way:
d(QR) = √[(x₂ - x₁)² + (y₂ - y₁)²]
d(QR) = √[(3 - (-7))² + (2 - 3)²]
d(QR) = √[10² + 1²]
d(QR) = √[100 + 1]
d(QR) = √101 ≈ 10.05 units (rounded to the nearest tenth)
The distance between points R(3,2) and P(-9,2) is simply the horizontal distance between the two points, as their y-coordinates are the same:
d(RP) = (-9 - 3) = -12 units (considering direction)
Now, let's sum up the lengths of the three sides of the triangle to find its perimeter:
Perimeter = d(PQ) + d(QR) + d(RP)
Perimeter = 2.24 + 10.05 + |-12|
Perimeter = 2.24 + 10.05 + 12
Perimeter = 24.29 units (rounded to the nearest tenth)
Therefore, the perimeter of △PQR is approximately 24.3 units (rounded to the nearest tenth).
To find the perimeter of a triangle, you need to add the lengths of all three sides of the triangle. In this case, triangle △PQR has vertices P(-9,2), Q(-7,3), and R(3,2).
To calculate the length of a side, you use the distance formula, which is the square root of the sum of the squares of the differences in x and y coordinates.
Let's calculate the length of each side and then add them up:
1. Side PQ:
- The difference in x-coordinates is (-9 - (-7)) = -2
- The difference in y-coordinates is (2 - 3) = -1
- The length of side PQ can be calculated as sqrt((-2)^2 + (-1)^2) = sqrt(4 + 1) = sqrt(5)
2. Side QR:
- The difference in x-coordinates is (-7 - 3) = -10
- The difference in y-coordinates is (3 - 2) = 1
- The length of side QR can be calculated as sqrt((-10)^2 + 1^2) = sqrt(100 + 1) = sqrt(101)
3. Side RP:
- The difference in x-coordinates is (3 - (-9)) = 12
- The difference in y-coordinates is (2 - 2) = 0
- The length of side RP can be calculated as sqrt(12^2 + 0^2) = sqrt(144 + 0) = sqrt(144)
Now, add up the lengths of all three sides: sqrt(5) + sqrt(101) + sqrt(144) ≈ 5.6 + 10.1 + 12 ≈ 27.6
Therefore, the perimeter of triangle △PQR is approximately 27.6 units.