Question

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

 (1, –1), (5, 2) and (9, 5)

Answer 1

Let A (1,-1), B(5,2)  and C(9,5) be the give points. Then

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

`BC = sqrt((9-5)^2 +(5-2)^2 ) = sqrt((4^2+3^2)) = sqrt(25)` = 5 units

`AC= sqrt((9-1)^2 +(5+1)^2) = sqrt(8^2+6^2) = sqrt(100)`=10 unit

∴ AB+BC = (5+5) units = 10 units = AC