Final answer:
The perimeter of triangle ABC is the sum of the lengths of sides AB, AC, and BC, which are calculated using the distance formula. The perimeter should be 12 units, but this is not one of the provided options.
Step-by-step explanation:
To find the perimeter of triangle ABC with vertices A(-4, -4), B(4, -4), and C(-4, -2), we will calculate the lengths of the sides of the triangle using the distance formula. The distance between two points (x1, y1) and (x2, y2) is given by the formula √((x2-x1)² + (y2-y1)²).
Firstly, the length of side AB is the distance between points A and B, which have the same y-coordinates. Thus, AB = |x2 - x1| = |4 - (-4)| = 8 units.
Secondly, the length of side AC is the distance between points A and C, which have the same x-coordinates. Thus, AC = |y2 - y1| = |-2 - (-4)| = 2 units.
Finally, side BC is also vertical like AC and has the same length, BC = AC = 2 units.
The perimeter P is the sum of the lengths of sides AB, AC, and BC: P = AB + AC + BC = 8 units + 2 units + 2 units = 12 units. However, none of the options given in the question (A. 14 units B. 24 units C. 114 units D. 28 units) match the calculated perimeter here. Therefore, the student or the question may have a mistake regarding the available options or coordinates.