Question

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

• A. $5x + y - 11= 0$
• B. $5x + 13y + 5 = 0$
• C. $5x -13y + 5 = 0$
• D. $13x -5y +5 = 0$

Answer 1

Answer: (A)

$5x + y - 11= 0$

Answer 2

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