Question

If the points A(x,y), B(3, 6) and C(−3,4) are collinear,show that x − 3y + 15 = 0

Answer 1

Since, the points A(x,y), B(3, 6) and C(−3,4) are collinear
Hence, the area of traiangle is zero.
$$\begin{gathered} \Rightarrow \frac{1}{2}\left[x_1\left(y_2-y_3\right)+x_2\left(y_3-y_1\right)+x_3\left(y_1-y_2\right)\right]=0 \\ \Rightarrow x\left(6-4\right)+3\left(4-y\right)-3\left(y-6\right)=0 \\ \Rightarrow 2x+12-3y-3y+18=0 \\ \Rightarrow 2x-6y+30=0 \\ \Rightarrow x-3y+15=0 \end{gathered}$$