question_answer

Two vertices of a triangle are (0, 2) and (4, 3). If its orthocenter is at the origin,  then its third vertex lies in which quadrant- [JEE Main Online Paper (Held On 10-Jan-2019 Evening]

A) third                             

B) fourth

C) second  

D)                  first

Correct Answer: C

Solution :

(BC and AD are perpendicular) \[\Rightarrow \,\,\frac{(k-2)}{h}\,=\,-\frac{4}{3}\,\,\Rightarrow \,3k\,-\,6\,=\,-4h\,\] \[\Rightarrow \,\,-12h-6=-4h\,\,\Rightarrow \,\,-6=8h\text{ }\Rightarrow \,\,h=-\frac{3}{4}\] \[\frac{k}{h}=-\,4\,\,\Rightarrow \,k=-\,4h\] \[k=-\,4\left( \frac{-3}{4} \right)\,\,\,\Rightarrow \,\,k=3\] \[B\left( \frac{-3}{4},\,\,3 \right)\]; IInd Quadrant