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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?
Options
third
second
first
fourth
MCQ
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Solution
Second
Explanation:
Let ΔPQR with orthocentre H
Let vertex R = (x, y)
Slopes; mQR × mPH = –1
⇒ mQR = `- 1/m_(PH)`
⇒ mQR = `(y - 3)/(x - 4)` = 0
⇒ y = 3
mPQ × mRH = –1
⇒ `1/4 xx y/x` = –1
⇒ y = –4x
⇒ x = `-3/4`
Vertex R is `((-3)/4, 3)`
Hence, vertex R lies in second quadrant.
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Equations of Line in Different Forms - Equations of Internal and External by Sectors of Angles Between Two Lines Co-ordinate of the Centroid, Orthocentre, and Circumcentre of a Triangle
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