Question

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

(6, 9), (0, 1) and (–6, –7)

Answer 1

Let A( 6,9) ,B( 0,1 )  and  C (-6, -7) be the give points. Then

`AB = sqrt((0-6)^2 +(1-9)^2 )= sqrt((-6)^2 +(-8)^2) = sqrt(36 + 64)= sqrt(100)`=10 units

`BC=sqrt((-6-0)^2+(-7-1)^2) = sqrt((-6)^2+(-8)^2)= sqrt(36 + 64)=  sqrt(100) `=10 units

`AC = sqrt((-6-6)^2 +(-7-9)^2 )= sqrt((-12)^2 +(16)^2) = sqrt(144 + 256 )= sqrt(400)`= 20 units

∴ AB + BC = (10+10) units - 20 units = AC

Hence, the given points are collinear