Question

Are the points (-1, 3), (1, 1), and (10, -8) on one line?

Answer 1

The three points are collinear i.e. they are on same line.

Explanation:

Three given points are on one line if the slopes of lines joining any of two pairs formed by them are equal .

As slope of line joining two points `(x_1,y_1)` and `(x_2,y_2)` is `(y_2-y_1)/(x_2-x_1)`.

As such slope of line joining `(-1,3)` and `(1,1)` is

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

and slope of line joining `(1,1)` and `(10,-8)` is

`(-8-1)/(10-1)=-9/9=-1`
graph{(x+y-2)((x+1)^2+(y-3)^2-0.04)((x-1)^2+(y-1)^2-0.04)((x-10)^2+(y+8)^2-0.04)=0 [-6, 12, -9, 4]}
(above graph not drawn to scale)

As the two slopes are same, the three points are collinear.