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

5 x + y - 11 = 0

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5 x + 13 y + 5 = 0

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5 x - 13 y + 5 = 0

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13 x - 5 y + 5 = 0

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Solution

The correct option is A $5 x + y - 11 = 0$
Since, the points $A (1, 6), B (3, - 4)$ and $C (x, y)$ are colinear
$∴$ $∣ ∣ ∣ ∣ \begin{matrix} 1 & 6 & 1 3 & - 4 & 1 x & y & 1 \end{matrix} ∣ ∣ ∣ ∣ = 0$
$\Rightarrow$ $1 (- 4 - y) - 6 (3 - x) + 1 (3 y + 4 x) = 0$
$\Rightarrow$ $10 x + 2 y - 22 = 0$
$\Rightarrow$ $5 x + y - 11 = 0$

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