ABC is a variable triangle such that A is (1, | vedclass

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(B) Let the coordinates of $A$ be $(1, 2)$.The line containing $B$ and $C$ is $L: x - y + \lambda = 0$.The altitude from $A$ to the line $BC$ is perpe

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$x + y = 3$

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(B) Let the coordinates of $A$ be $(1, 2)$.The line containing $B$ and $C$ is $L: x - y + \lambda = 0$.The altitude from $A$ to the line $BC$ is perpendicular to $BC$.The slope of $BC$ is $m = 1$.Therefore,the slope of the altitude from $A$ is $m' = -1$.The equation of the altitude from $A$ is $y - 2 = -1(x - 1)$,which simplifies to $y - 2 = -x + 1$,or $x + y = 3$.Since the orthocenter of a triangle always lies on its altitudes,and the altitude from $A$ is fixed regardless of the value of $\lambda$,the locus of the orthocenter is the line $x + y = 3$.

$ABC$ is a variable triangle such that $A$ is $(1, 2)$,and $B$ and $C$ lie on the line $y = x + \lambda$ (where $\lambda$ is a variable). The locus of the orthocenter of triangle $ABC$ is:

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