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The points A(1, 5), B(2, 3) and C(-2, 11) are:

  • A.Collinear
  • B.Vertices of a scalene triangle
  • C.Vertices of an isosceles triangle
  • D.None of the above

Answer: A

Three points are collinear if the slope between any two pairs of points is the same.

Slope of AB = \(\frac{y_2 - y_1}{x_2 - x_1} = \frac{3 - 5}{2 - 1} = \frac{-2}{1} = -2\).

Slope of BC = \(\frac{y_3 - y_2}{x_3 - x_2} = \frac{11 - 3}{-2 - 2} = \frac{8}{-4} = -2\).

Since the slope of AB is equal to the slope of BC, the points A, B, and C lie on the same straight line and are collinear.

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