A) (-3, 1)
B) (-1, 1/3)
C) (1, 3)
D) None of these
Correct Answer: C
Solution :
Let \[A(-2,-6),B(-2,\,4)\,C(1,\,3)\] be the vertices of the triangle. Slope of \[BC=\frac{3-4}{1+2}=\frac{-1}{3}\] Slope of \[\bot \] to \[BC=3\] Equation of altitude through A is \[y+6=3(x+2)\] Þ \[y+6=3x+6\] Þ \[y=3x\] .....(i) Slope of \[CA=\frac{3+6}{1+2}=\frac{9}{3}=3\] Slope of \[\bot \] to \[CA=\frac{-1}{3}\] Equation of altitude through B is \[y-4=\frac{-1}{3}(x+2)\] Þ \[3y-12=-x-2\] Þ \[x+3y-10=0\] .....(ii) Solving (i) and (ii)\[x=1,y=3\] Hence, orthocentre (1, 3).
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