Question

Find a relation between x and y if the points A(2, 1), B(x, y) and C(7, 5) are collinear.

Answer 1

Consider the points A(2, 1), B(x, y) and C(7, 5) .
Here, (x₁ = 2, y₁ = 1), (x₂ = x, y₂ = y) and (x₃ = 7, y₃ = 5).
It is given that the points are collinear. So,
$$\begin{gathered} x_1\left(y_2-y_3\right)+x_2\left(y_3-y_1\right)+x_3\left(y_1-y_2\right)=0 \\ \Rightarrow 2\left(y-5\right)+x\left(5-1\right)+7\left(1-y\right)=0 \\ \Rightarrow 2y-10+5x-x+7-7y=0 \\ \Rightarrow 4x-5y-3=0 \end{gathered}$$