Using the distance formula, show that the points A(3, -2), B(5, 2) and C(8,8) are collinear.

Given: The 3 points are A(3, -2), B(5, 2) and C(8, 8).

AB

= 2√5 units …..(1)

BC

= 3√5 units …..(2)

AC

= 5√5 units …..(3)

From equations 1, 2 and 3, we have

⇒ AC = AB + BC

This is possible only if the points are collinear.

Therefore, the points A, B and C are collinear.

Hence, proved.