Using determinants prove the following points are collinear..

  1. (11,7),(5,5),(-1,3)
  2. (0,3),(4,6),(-8,-3)
  3. (-2,5),(-6,-7),(-5,-4)

Let A(x1, y1), B(x2, y2) and C(x3, y3) be three point. Then, A, B, C are collinear, if

1. 

Let the given point be A(11, 7), B(5, 5) and C(– 1, 3).

Expanding along C3, we have

Δ = 0 – 0 + 1 × (12 × 2 – 6 × 4) = 0 – 0 + (24 – 24) = 0 – 0 + 0 = 0

Hence, the point A(11, 7), B(5, 5) and C(– 1, 3) are collinear.

 

Similarly, you can solve the remaining two parts of the question.

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