Discussion
The points (2, -2), (-2, 1), and (5, 2) are the vertices of a:
Answer: A
Let's find the slopes of the lines connecting the points.
Slope between (2,-2) and (-2,1) = \(\frac{1-(-2)}{-2-2} = \frac{3}{-4}\).
Slope between (-2,1) and (5,2) = \(\frac{2-1}{5-(-2)} = \frac{1}{7}\).
Slope between (5,2) and (2,-2) = \(\frac{-2-2}{2-5} = \frac{-4}{-3} = \frac{4}{3}\).
The product of the slopes of the first and third lines is \((-\frac{3}{4}) \times (\frac{4}{3}) = -1\). Since the product is -1, these two lines are perpendicular, forming a right angle. Therefore, the triangle is a right-angled triangle.
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