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In $Δ A B C$ if $A = (1, 2), B$ and C lie on $y = x + α$ (where $α$ is variable) then the locus of orthocentre of the triangle is

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$x + y - 3 = 0$

$x + y + 3 = 0$

$y = x + 1$

$y = x - 1$

answer is A.

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Detailed Solution

$\begin{array}{l} m_{B C} \cdot m_{A D} = - 1 \\ \Rightarrow m_{A D} = - 1 \end{array}$
Equation AD is $y - 2 = - 1 (x - 1)$
$x + y - 3 = 0$

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