A) \[(3,\,1)\]
B) \[(1,\,1/3)\]
C) \[(1,3)\]
D) None of these
Correct Answer: C
Solution :
Let the vertices of the triangle are \[A(-2,-6),B(-2,4)\] and \[C(1,3)\] Now, \[AB=\sqrt{{{(-2+2)}^{2}}+{{(-6-4)}^{2}}}=10\] \[BC=\sqrt{{{(-2-1)}^{2}}+{{(4-3)}^{2}}}=\sqrt{10}\] and \[CA=\sqrt{{{(1+2)}^{2}}+{{(3+6)}^{2}}}=\sqrt{90}\] Here, \[A{{B}^{2}}=B{{C}^{2}}+C{{A}^{2}}\] \[\therefore \] Triangle is right angled triangle at C. \[\therefore \] \[\angle C={{90}^{o}}\] So, orthocenter is \[(1,3).\]
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