I think I got forgotten...
What is the perimeter of triangle PQR with vertices P(–2, 9), Q(7, –3), and R(–2, –3) in the coordinate plane? (1 point)
21 units
25 units - ??
34 units
36 units
36 units, right?
Yes
First draw out your triangle .
It gives you the length of two of the side
Vertices (-2,9) and (-2,-3) have the same x values so the line is straight up and down. Find the distance between the y values to find the length of that side
Vertices (-2,-3) and (7,-3) have the same y values. Find the difference in x values to find that length.
Then use the Pythagorean Theorem to find the last side
Then add all the side lengths for the perimeter
Thank you
Ah, don't worry! You haven't been forgotten. It seems like you're having a triangle dilemma! Let's solve it together.
To find the perimeter of a triangle, we need to add up the lengths of all three sides. So, let's calculate the distances between the given vertices.
Using the distance formula, the length of side PQ is:
√[(7 - (-2))^2 + (-3 - 9)^2] = √(9^2 + (-12)^2)
The length of side PR is:
√[(-2 - (-2))^2 + (-3 - 9)^2] = √(0^2 + (-12)^2)
The length of side RQ is:
√[(7 - (-2))^2 + (-3 - (-3))^2] = √(9^2 + 0^2)
Now, let's add them up:
√(81 + 144) + √(0 + 144) + √(81 + 0) = √(225) + √(144) + √(81)
= 15 + 12 + 9
= 36 units!
So, the perimeter of triangle PQR is indeed 36 units. Keep those math skills sharp!
To find the perimeter of a triangle, we need to find the sum of the lengths of its sides. The length of a side can be found using the distance formula, which is
distance = √[(x2 - x1)^2 + (y2 - y1)^2]
Let's calculate the lengths of the sides of triangle PQR:
1. Side PQ:
distance = √[(7 - (-2))^2 + (-3 - 9)^2]
= √[9^2 + (-12)^2]
= √[81 + 144]
= √225
= 15 units
2. Side QR:
distance = √[(-2 - 7)^2 + (-3 - (-3))^2]
= √[(-9)^2 + 0^2]
= √[81 + 0]
= √81
= 9 units
3. Side RP:
distance = √[(-2 - (-2))^2 + (-3 - 9)^2]
= √[0^2 + (-12)^2]
= √[0 + 144]
= √144
= 12 units
Now, let's calculate the perimeter by summing up the lengths of the sides:
Perimeter = PQ + QR + RP
= 15 + 9 + 12
= 36 units
Therefore, the correct answer is 36 units.