A) \[(4,7)\]
B) \[(3,7)\]
C) \[(-4,-7)\]
D) \[(4,-\,7)\]
Correct Answer: C
Solution :
[c]Slope of \[AH=\frac{k}{h}\] |
Slope of\[BC=\frac{4}{-\,7}\] |
Slope of \[AH\times \]slope of \[BC=-1\] |
\[\therefore \] \[\frac{k}{h}\times \frac{4}{-\,7}=-1\] |
\[\frac{k}{h}=\frac{7}{4}\] ? (i) |
Slope of \[AC=\frac{k+1}{h-5}\] |
Slope of \[BH=\frac{-\,3}{2}\] |
Slope of \[AC\times \]Slope of \[BH=-\,1\] |
\[\therefore \] \[\left( \frac{k+1}{h-5} \right)\left( \frac{-\,3}{2} \right)=-1\] |
\[\Rightarrow \] \[\frac{k+1}{h-5}=\frac{2}{3}\] ? (ii) |
On solving Eqs. (i) and (ii), we get \[h=-\,4,k=-\,7\] |
\[\therefore \]Third vertex of triangle is \[(-\,4,-7).\] |
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