Question

Show that the points (1, 3), (2, 1) and `(1/2, 4)` are collinear, by using a straight line

Answer 1

Let the given points be A (1 , 3), B (2 , 1) and `"C"(1/2, 4)`

Using a straight line

A(1, 3), B(2, 1), `"C"(1/2, 4)` 

The equation of the straight line joining the points

A(1, 3), B(2, 1) is

`(x - 1)/(2 - 1) = (y - 3)/(1 - 3)`

`(x - 1)/1 = (y - 3)/(- 2)`

– 2(x – 1) = y – 3

– 2x + 2 = y – 3

2x + y – 2 – 3 = 0

2x + y – 5 = 0  .......(2)

Substituting the third point `"C"(1/2, 4)` in equation (2)

We have `2(1/2) + 4 - 5` = 0

1 + 4 – 5 = 0

0 = 0

∴ The third point `"C"(1/2, 4)` lies on the straight line AB.

Hence the points A, B, C are collinear.