In triangle ABC,if A is (1,2),and B and C lie | vedclass

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(A) Let $H(h, k)$ be the orthocenter of $	riangle ABC$. The orthocenter is the intersection of the altitudes. Since $B$ and $C$ lie on the line $y=x+

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$x+y-3=0$

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(A) Let $H(h, k)$ be the orthocenter of $	riangle ABC$. The orthocenter is the intersection of the altitudes. Since $B$ and $C$ lie on the line $y=x+\alpha$,the line $BC$ has a slope of $1$. The altitude from $A(1, 2)$ to $BC$ must be perpendicular to $BC$. Therefore,the slope of the altitude $AD$ is $-1$. The equation of the altitude $AD$ passing through $A(1, 2)$ with slope $-1$ is $y-2 = -1(x-1)$,which simplifies to $y-2 = -x+1$,or $x+y-3=0$. Since the orthocenter $H(h, k)$ must lie on this altitude,its locus is $x+y-3=0$.

In $\triangle ABC$,if $A$ is $(1,2)$,and $B$ and $C$ lie on the line $y=x+\alpha$ (where $\alpha$ is a variable),then the locus of the orthocenter of the triangle is:

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