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Question
If two vertices of a triangle are (5,−1) and (−2,3) and if the orthocenter lies at the origin, then co-ordinates of third vertex are
If two vertices of a triangle are (5,−1) and (−2,3) and if the orthocenter lies at the origin, then co-ordinates of third vertex are
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Solution
The correct option is B (−4,−7)
Let the cordinates of vertex of triangle are A(h,k)
As it is clearly seen from the figure thatline A0⊥BCSlope of AO× Slope of BC=-1k−0h−0×3−(−1)−2−5=−1
kh=74
→7h=4k ‘−(1)
Also line BO⊥ACsimilarly −1−05−0×k−3h−(−2)=−1
k−3h+2=5k−3=5h+10
→k=5h+13 ‘−(2)On solving eqs. (1) and (2) we get, h=-4 and k=-7Therefore the required vertex is (-4,-7)
Let the cordinates of vertex of triangle are A(h,k)
As it is clearly seen from the figure that
line A0⊥BC
Slope of AO× Slope of BC=-1
k−0h−0×3−(−1)−2−5=−1
kh=74
→7h=4k ‘−(1)
Also line BO⊥AC
similarly
−1−05−0×k−3h−(−2)=−1
k−3h+2=5
k−3=5h+10
→k=5h+13 ‘−(2)
On solving eqs. (1) and (2) we get, h=-4 and k=-7
Therefore the required vertex is (-4,-7)
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