Question

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

(–1, –1), (2, 3) and (8, 11)

Answer 1

Let A(-1, -1) , B(2,3) and C( 8,11) be the give points. Then

`AB = sqrt((2+1)^2 +(3+1)^2) = sqrt((3)^2 +(4)^2) = sqrt(25)` =5 units

`BC=sqrt((8-2)^2 +(11-3)^2 = sqrt(6)^2 +(8)^2 = sqrt(100) `= 10 units

`AC = sqrt(( 8+1)^2 +(11+1)^2 ) = sqrt((9)^2 +(12)^2 = sqrt(225) `= 15 units

∴ AB +BC = (5+10)  units  = 15 units   = Ac

Hence, the given points are collinear