What is the perimeter of △PQR

Question

 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

Answer 1

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.