If the points `A(x , y),B(3,6)a n dC(-3,4)` are collinear, show that `x-3y+15=0`

Explanation

Given: ` A(x, y), B(3,6) and C(-3,4)` are collinear, then


Area of the triangle `\triangle\ {ABC}=0`


Hence, `frac{1}{2}[x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)]=0 `


`Rightarrow x(6-4)+3(4-y)+(-3)(y-6)=0 `


`Rightarrow 2 x+12-3 y-3 y+18=0`


`Rightarrow 2 x-6 y+30=0`


`Rightarrow 2(x-3 y+15)=0 `


`Rightarrow x-3 y+15=0`