Question:
Using slopes show that the points A(6, -1), B(5, 0) and C(2, 3) are collinear.
Solution:
For three points to be collinear, the slope of all pairs must be equal, that is the slope of AB = slope of BC = slope of CA
Given points are A(6, -1), B(5, 0) and C(2, 3)
slope $=\left(\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\right)$
Slope of $A B=\left(\frac{0+1}{5-6}\right)=\frac{1}{-1}=-1$
Slope of $B C=\left(\frac{3-0}{2-5}\right)=\frac{3}{-3}=-1$
Slope of $C A=\left(\frac{3+1}{2-6}\right)=\frac{4}{-4}=-1$
Therefore slopes of AB, BC and CA are equal, so Points A,B,C are collinear.