Question

Verify whether the following points are collinear or not:

A(1, –3), B(2, –5), C(–4, 7). 

Answer 1

A ≡ (1, –3) ≡ (x₁ ,y₁),

B ≡ (2, –5) ≡ (x₂, y₂),

C ≡ (–4, 7) ≡ (x₃, y₃).  

Slope of AB = ` (y_2 - y_1)/(x_2 - x_2)`

`=(-5 - (-3))/(2 - 1)`

`= (-5 + 3)/(2 - 1)`

= `(-2)/1`

= –2

Slope of BC = `(y_3 - y_2)/(x_3 - x_2)` 

`= (7 - (-5))/(-4 - 2)`

= `(7 + 5)/(-4-2)`

`= 12/-6`

= –2

A, B, and C are collinear points that have B as a common point.