Question

Using slope concept, check whether the following points are collinear.
A(7, 8), B(−5, 2) and C(3, 6).

Answer 1

The given points are A(7, 8), B(−5, 2) and C(3, 6).
Here, x₁ = 7, y₁ = 8, x₂ = −5, y₂ = 2, x₃ = 3 and y₃ = 6
Now, we will find the slopes of the AB and BC.

$$\begin{gathered} \mathrm{Slope}\mathrm{of}AB=\frac{y_2-y_1}{x_2-x_1} \\ =\frac{2-8}{-5-7} \\ =\frac{6}{12} \\ =\frac{1}{2} \end{gathered}$$

$$\begin{gathered} \mathrm{Slope}\mathrm{of}BC=\frac{y_3-y_2}{x_3-x_2} \\ =\frac{6-2}{3-(-5)} \\ =\frac{4}{8} \\ =\frac{1}{2} \end{gathered}$$

Here, the slope of AB is the same that of BC and point B is common to both AB and BC.
∴ Points A, B and C are collinear.