Final answer:
After calculating the lengths of the sides of the triangle with the distance formula, it is found that two sides are equal and one is different. Thus, the triangle is classified as an isosceles triangle.
Step-by-step explanation:
To classify the triangle with vertices A(2,-2), B(0,4), and C(-4,-4) by its sides, we must calculate the lengths of the triangle's sides using the distance formula. The distance between two points (x1, y1) and (x2, y2) is given by √((x2-x1)^2 + (y2-y1)^2).
First, let's find the length of side AB:
√((0-2)^2 + (4+2)^2) = √(4 + 36) = √40 ≈ 6.32
Next, calculate the length of side BC:
√((-4-0)^2 + (-4-4)^2) = √(16 + 64) = √80 ≈ 8.94
Finally, we determine the length of side CA:
√((-4-2)^2 + (-4+2)^2) = √(36 + 4) = √40 ≈ 6.32
Comparing these lengths, we find that two sides (AB and CA) are equal while the third side (BC) is of different length. Therefore, the triangle is classified as an isosceles triangle. The correct answer is B) Isosceles.