Question

Use distance formula to show that the points A(-1, 2), B(2, 5) and C(-5, -2) are collinear.

Answer 1

If using distance formula we have to prove that A, B and C are collinear, then we  have to show:
BC = AC + AB
Hence AB = `sqrt((5 - 2)^2 + (2 + 1)^2) = sqrt(9 + 9)`
= `sqrt(18) = 3sqrt(2)"units"`.
BC = `sqrt((-2 - 5)^2 + (- 5 - 2)^2)`
= `sqrt(49 + 49) = sqrt(98) = 7sqrt(2)"units"`.
and AC = `sqrt((-2 - 2)^2 + (-5 + 1)^2)`
= `sqrt(16 + 16) = sqrt(32) = 4sqrt(2)"units"`.
as `7sqrt(2) = 4sqrt(2) + 3sqrt(2)`
⇒ BC = AB + AC
⇒ Points A,B and C are collinear.
Hence proved.