Question

Using the slope concept check whether the following points are collinear
A($-$1, 8), B(9, $-$2) and C(3, 4).

Answer 1

The given points are A($-$1, 8), B(9, $-$2) and C(3, 4).

Here, x₁ = $-$1, y₁ = 8, x₂ = 9, y₂ = $-$2, x₃ = 3 and y₃ = 4
Now, we will find the slopes.

$$\begin{gathered} \mathrm{Slope}ofAB=\frac{y_2-y_1}{x_2-x_1} \\ =\frac{-2-8}{9-(-1)} \\ =\frac{-10}{10} \\ =-1 \end{gathered}$$

$$\begin{gathered} \mathrm{Slope}ofBC=\frac{y_3-y_2}{x_3-x_2} \\ =\frac{4-(-2)}{3-9} \\ =\frac{6}{-6} \\ =-1 \end{gathered}$$

Since the slopes in both the cases are equal, the points are collinear.