Question

Using the distance formula, show that the given points are collinear:

(–2, 5), (0, 1) and (2, –3)

Answer 1

Let A( -2,5) , B(0,1) and C (2, -3) be the give points. Then

`AB= sqrt((0+2)^2 +(1+5)^2 ) = sqrt((2)^2 +(-4)^2) = sqrt(20) = 2 sqrt(5) `units

`BC = sqrt((2-0)^2 + (-3-1)^2) = sqrt((2)^2+(-4)^2) = sqrt(20) = 2 sqrt(5)` units

`AC= sqrt((2+2)^2 +(-3-5)^2) = sqrt((4)^2 +(-8)^2) = sqrt(80) = 4sqrt(5) `units

`∴ AB +BC = (2 sqrt(5)+2 sqrt(5))   units  = 4 sqrt(5)   units   = Ac`

Hence, the given points are collinear