Question

Show that the following sets of points are collinear. 

(2, 5), (4, 6) and (8, 8)

Answer 1

The formula for the area ‘A’ encompassed by three points, (x₁,y₁) (x₂,y₂)and (x₃,y₃) is given by the formula,

We know area o triangle formed by three points (x₁,y₁),(x_2,y₂),(x₃,y₃) is given by  

`Δ=1/2[x_1(y_2-y_3)+x_2 (y_3-y_1)+x_3(y_1-y_2)] `

If three points are collinear the area encompassed by them is equal to 0 

The three given points are A(2, 5), B(4, 6) and C(8, 8). Substituting these values in the earlier mentioned formula we have, 

A`=1/2[2(6-8)+4(8-5)+8(5-6)] `

`=1/2[2(-2) +4(3)+8(-1)]` 

`=1/2[-4+12-8]`   

`=1/2 [-12+12]`

`=0`

Since the area enclosed by the three points is equal to 0, the three points need to be colliner