Answer:
2 + √[26] + √[50]
Explanation:
To find the perimeter of a triangle with vertices given in the coordinate plane, we need to calculate the distance between each pair of vertices and then add them up.
Using the distance formula, the distance between the first two vertices is:
√[(x2 - x1)^2 + (y2 - y1)^2] =
√[(-4 - (-4))^2 + (1 - 3)^2] =
√[0 + 4] = 2
The distance between the second and third vertices is:
√[(x2 - x1)^2 + (y2 - y1)^2] =
√[(-5 - (-4))^2 + (-4 - 1)^2] =
√[1 + 25] = √[26]
Finally, the distance between the third and first vertices is:
√[(x2 - x1)^2 + (y2 - y1)^2] =
√[(-4 - (-5))^2 + (3 - (-4))^2] =
√[1 + 49] = √[50]
Therefore, the perimeter of the triangle is:
2 + √[26] + √[50]
This is the exact answer, and we cannot simplify it further.