Question

Using the slope concept check whether the following points are collinear
A(4,$-$5), B(7, 8) and C($-$2,$-$3).

Answer 1

The given points are A(4,$-$5), B(7, 8) and C($-$2,$-$3).

Here, x₁ = 4, y₁ = $-$5, x₂ = 7, y₂ = 8, x₃ = $-$2 and y₃ = $-$3
Now, we will find the slopes.

$$\begin{gathered} \mathrm{Slope}ofAB=\frac{y_2-y_1}{x_2-x_1} \\ =\frac{8-(-5)}{7-4} \\ =\frac{13}{3} \end{gathered}$$

$$\begin{gathered} \mathrm{Slope}ofBC=\frac{y_3-y_2}{x_3-x_2} \\ =\frac{-3-8}{-2-7} \\ =\frac{-11}{-9} \\ =\frac{11}{9} \end{gathered}$$

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