Question

Using the slope concept, check whether the following points are collinear
A(0, 6), B(3, 0) and C(2 , 4).

Answer 1

The given points are A(0, 6), B(3, 0) and C(2 , 4).

Here, x₁ = 0, y₁ = 6, x₂ = 3, y₂ = 0, x₃ = 2 and y₃ = 4
Now, we will find the slopes.

$$\begin{gathered} \mathrm{Slope}ofAB=\frac{y_2-y_1}{x_2-x_1} \\ =\frac{0-6}{3-0} \\ =\frac{-6}{3} \\ =-2 \end{gathered}$$

$$\begin{gathered} \mathrm{Slope}ofBC=\frac{y_3-y_2}{x_3-x_2} \\ =\frac{4-0}{2-3} \\ =\frac{4}{-1} \\ =-4 \end{gathered}$$

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