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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

A
(4,7)
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B
(4,7)
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C
(2,3)
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D
(5,1)
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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 that
line A0BC
Slope of AO× Slope of BC=-1
k0h0×3(1)25=1

kh=74

7h=4k (1)

Also line BOAC
similarly
1050×k3h(2)=1

k3h+2=5
k3=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)

1909145_1172650_ans_54774ff9ce624aee850a48b4c2c88169.png

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