Question

Using the slope concept check whether the following points are collinear
A($-$1, 2), B(3, 4) and C(5,$-$6).

Answer 1

The given points are A($-$1, 2), B(3, 4) and C(5,$-$6).

Here, x₁ = $-$1, y₁ = 2, x₂ = 3, y₂ = 4, x₃ = 5 and y₃ = $-$6
Now, we will find the slopes.

$$\begin{gathered} \mathrm{Slope}ofAB=\frac{y_2-y_1}{x_2-x_1} \\ =\frac{4-2}{3-(-1)} \\ =\frac{2}{4} \\ =\frac{1}{2} \end{gathered}$$

$$\begin{gathered} \mathrm{Slope}ofBC=\frac{y_3-y_2}{x_3-x_2} \\ =\frac{-6-4}{5-3} \\ =\frac{-10}{2} \\ =-5 \end{gathered}$$

Since the slopes in the both cases are not equal, the points are not collinear.