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  4. If the three points A(1,6), B(3, -4) and C(x, y) are collinear then the equation satisfying by x and y is

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Q. If the three points $A(1,6), B(3, -4)$ and $C(x, y)$ are collinear then the equation satisfying by $x$ and $y$ is

WBJEEWBJEE 2011Straight Lines

Solution:

Since, the points $A(1,6), B(3,-4)$ and $C(x, y)$ are collinear.
$\therefore \begin{vmatrix}1 & 6 & 1 \\ 3 & -4 & 1 \\ x & y & 1\end{vmatrix}=0$
$\Rightarrow 1(-4-y)-6(3-x)+1(3 y+4 x)=0$
$\Rightarrow 10 x+2 y-22=0$
$\Rightarrow 5 x+y-11=0$