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  4. A B C is a variable triangle such that A is (1,2), and B and C lie on the line y=x+λ(λ is a variable). Then the locus of the or thocenter of triangle A B C is

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Q. $A B C$ is a variable triangle such that $A$ is $(1,2)$, and $B$ and $C$ lie on the line $y=x+\lambda(\lambda$ is a variable). Then the locus of the or thocenter of $\triangle A B C$ is

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Solution:

As the altitude from $A$ is fixed and the orthocenter lies on the altitude, $x + y = 3$ is the required locus.