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
mAD⋅mBC=−1⇒mAH⋅mBC=−1 ⇒(y−0x−0)⋅(3−24−0)=−1 ⇒4x+y=0⋯(1)
Now, mBE⋅mAC=−1⇒mBH⋅mAC=−1 ⇒(3−04−0)⋅(y−2x−0)=−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.