Final answer:
The perimeter of a triangle with points D(-4, -3), E(1, 0), and F(-2, 2) is found by summing the distances between each pair of points, resulting in \sqrt{34} + \sqrt{13} + \sqrt{29} units.
Step-by-step explanation:
We will find the perimeter of a triangle with the following points: D(-4, -3), E(1, 0), and F(-2, 2). To do this, we must calculate the distance between each pair of points to find the lengths of the sides of the triangle, and then sum these lengths to obtain the perimeter.
To calculate the distance between two points (x1, y1) and (x2, y2), we use the distance formula: .
The lengths of the sides of the triangle can be calculated as follows:
DE: \sqrt{(1 - (-4))^2 + (0 - (-3))^2} = \sqrt{5^2 + 3^2} = \sqrt{25 + 9} = \sqrt{34}
EF: \sqrt{(-2 - 1)^2 + (2 - 0)^2} = \sqrt{(-3)^2 + 2^2} = \sqrt{9 + 4} = \sqrt{13}
FD: \sqrt{(-2 - (-4))^2 + (2 - (-3))^2} = \sqrt{2^2 + 5^2} = \sqrt{4 + 25} = \sqrt{29}
Now, we sum the lengths of DE, EF, and FD to find the perimeter:\sqrt{34} + \sqrt{13} + \sqrt{29}
Therefore, the perimeter of the triangle is \sqrt{34} + \sqrt{13} + \sqrt{29} units.