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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?
  1. first
  2. third
  3. fourth
  4. second


Solution

The correct option is D 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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