Question

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

Answer 1

Slop of line AB = m = ${\displaystyle \frac{2-3}{0-1(-1)}=\frac{-1}{1}=-1}$

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

y – y₁ = m(x – x₁)

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 = ${\displaystyle \frac{1-2}{1-0}=-\frac{1}{1}=-1}$

Since, slope of line AB = slope of line BC.

Point A, B and C are collinear.