Prove that the points A(1, 4), B(3, - 2) and C(4, - 5) are collinear. Also, find the equation of the line on which these points lie.

Question

Philoid · Accepted Answer

If two lines having the same slope pass through a common point, then two lines will coincide. Hence, if A, B and C are three points in the XY - plane, then they will lie on a line, i.e., three points are collinear if and only if slope of AB = slope of BC.

Slope of AB = slope of BC

- 3 = - 3

Hence verified, i.e. points are collinear. Now using two point form of the equation

y - 4 = - 3(x - 1)

y - 4 + 3x - 3 = 0

3x + y - 7 = 0

So, required equation of line is 3x + y - 7.