Show that the points (1, 1), (-2, 7) and (3, -3) are collinear.

Let A(1, 1), B(-2, 7) and C(3, -3) be the three points.

As the points are collinear, area of triangle ABC is zero.
The condition for collinearity of three given points (x ₁ , y ₁ ), (x ₂ , y ₂ ) and (x ₃ , y ₃ ) is
x ₁ (y ₂ – y ₃ ) + x ₂ (y ₃ – y ₁ ) + x ₃ (y ₁ – y ₂ ) = 0.

Taking L.H.S.: 1× (7 – (-3)) + (-2)×(-3 – 1) + 3×(1 – 7)

= 10 + 8 -18

= 0

= R.H.S.

Hence A, B, C are collinear.