Question

Can we use the slope method to prove that the points are collinear, If yes how do we do it?

Answer 1

Dear student,

If the line segments AB and BC have the same slope, then A, B, C are necessarily collinear. Note that there are some corner cases having to do with whether B is the "middle" point or not (in which case the slopes will still be equal), and one having to do with vertical lines (where some formula you use to compute slope might divide by 0).

$$\begin{gathered} Puttingallthistogether,thepoint(a,b)(m,n)and(x,y)arecollinear \\ ifandonlyif \\ \left(n-b\right)\left(x-m\right)=(y-n)(m-a) \end{gathered}$$

Regards