Question

Show that the points (1, 3), (2, 1) and `(1/2, 4)` are collinear, by using concept of slope 

Answer 1

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

Slope Method:

A (1 , 3 ), B (2 , 1 ), `"C"(1/2, 4)`

Slope of AB = `(1 - 3)/(2 - 1)`

= `(-2)/1`

= – 2     .......(1)

Slope of BC = ``(4 - 1)/(1/2 - 2)`

= `3/((1 - 4)/2)`

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

= – 2     .......(2)

From equations (1) and (2)

Slope of AB = Slope of BC

∴ The given points A, B, C are collinear.