Which of the following statements is true about the point A(-4, -2), B(1, 4) and C(6, 11)?
- The points form an isosceles triangle
- The points are collinear
- The points form a scalene triangle
- None of these
Explanation
The points form a scalene triangle:
Calculate the distances AB, BC, and AC. If all sides are unequal, it's a scalene triangle.
AB = √((1 - (-4))² + (4 - (-2))²) = √(5² + 6²) = √61
BC = √((6 - 1)² + (11 - 4)²) = √(5² + 7²) = √74
AC = √((6 - (-4))² + (11 - (-2))²) = √(10² + 13²) = √269
All sides are unequal (√61 ≠ √74 ≠ √269), so the points form a scalene triangle.
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