Final answer:
The triangle formed by points A(-2,3), B(0,-3), and C(3,-2) can be classified as a scalene triangle, as all three sides have different lengths, calculated with the distance formula.
Step-by-step explanation:
To classify the triangle formed by points A(-2,3), B(0,-3), and C(3,-2) by its sides, we need to calculate the lengths of the sides using the distance formula. The distance between two points (x1, y1) and (x2, y2) is given by √[(x2-x1)² + (y2-y1)²].
For side AB: √[(0-(-2))² + (-3-3)²] = √[2² + (-6)²] = √[4 + 36] = √40.
For side BC: √[(3-0)² + (-2-(-3))²] = √[3² + 1²] = √[9 + 1] = √10.
For side AC: √[(3-(-2))² + (-2-3)²] = √[5² + (-5)²] = √[25 + 25] = √50.
With the lengths of the sides calculated, we see that the triangle has three sides of different lengths (√40, √10, and √50), so this triangle can be classified as a scalene triangle.
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