The perimeter of the triangle is 21.4 units
<h3>How to determine the perimeter?</h3>
The points are given as:
A(−2,2), B(5,−3), and C(−4,−1)
Calculate the side lengths using:
![d = \sqrt{(x_2 -x_1)^2 + (y_2 -y_1)^2](https://tex.z-dn.net/?f=d%20%3D%20%5Csqrt%7B%28x_2%20-x_1%29%5E2%20%2B%20%28y_2%20-y_1%29%5E2)
So, we have:
![AB = \sqrt{(-2 -5)^2 + (2 + 3)^2} = 8.6](https://tex.z-dn.net/?f=AB%20%3D%20%5Csqrt%7B%28-2%20-5%29%5E2%20%2B%20%282%20%2B%203%29%5E2%7D%20%3D%208.6)
![AC = \sqrt{(-2 +4)^2 + (2 + 1)^2} = 3.6](https://tex.z-dn.net/?f=AC%20%3D%20%5Csqrt%7B%28-2%20%2B4%29%5E2%20%2B%20%282%20%2B%201%29%5E2%7D%20%3D%203.6)
![BC = \sqrt{(5+4)^2 + (-3 + 1)^2} = 9.2](https://tex.z-dn.net/?f=BC%20%3D%20%5Csqrt%7B%285%2B4%29%5E2%20%2B%20%28-3%20%2B%201%29%5E2%7D%20%3D%209.2)
The perimeter is then calculated as:
P = AB + AC + BC
This gives
P = 8.6 + 3.6 + 9.2
Evaluate
P = 21.4
Hence, the perimeter of the triangle is 21.4 units
Read more about perimeter at:
brainly.com/question/24571594
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