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Question

Two vertices of a triangle are (0,2) and (4,3). If its orthocentre is at the origin, then its third vertex lies in which quadrant?

A
first
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B
second
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C
third
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D
fourth
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Solution

The correct option is B second

mADmBC=1mAHmBC=1
(y0x0)(3240)=1
4x+y=0 (1)
Now,
mBEmAC=1mBHmAC=1
(3040)(y2x0)=1
4x+3y=6 (2)
from the equations (1) and (2), we get
x=34, y=3
Hence, Point (x,y) lies in second quadrant.

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