Find the Equation of the Line Through the Points A(-1,3) and B(0,2). Hence, Show that the Pointa,B and C (1,1) Are Collinear. - Mathematics

Sum

Find the equation of the line through the points A(-1,3) and B(0,2). Hence, show that the pointA,B and C (1,1) are collinear.

Slop of line AB=m=` (2-3)/(0-1(-1))=(-1)/1=-1`

Using the slope-point from, the equation of line Ab is given by

`y-y_1=m(x-x_1)`

i.e. `y-3=-1[x-(-1)]`

i.e.`y-3=-1(x+1)`

i.e.`y-3=-x-1`

i.e.` x+y=2`

Now, slope of line` BC=(1-2)/(1-0)=-1/1=-1`

Since, slope of line Ab= slope of line BC, Point A, B and C are collinear.

Concept: General Equation of a Line

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Chapter 14 Equation of a Line
Exercise 14 (E) | Q 37 | Page 204