Question

Using the slope concept check whether the following points are collinear
A(7,$-$1), B(0, 3) and C(4,0).

Answer 1

The given points are A(7,$-$1), B(0, 3) and C(4,0).

Here, x₁ = 7, y₁ = $-$1, x₂ = 0, y₂ = 3, x₃ = 4 and y₃ = 0
Now, we will find the slopes.

$$\begin{gathered} \mathrm{Slope}ofAB=\frac{y_2-y_1}{x_2-x_1} \\ =\frac{3-(-1)}{0-7} \\ =\frac{4}{-7} \\ =\frac{-4}{7} \end{gathered}$$

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

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