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QJEEM19Ma94ae: JEE Main 2019 Mathematics - Class 11 JEEM19Ma94ae Solution: Two vertices of a triangle are (0, 2) and (4, 3). If its…

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

Multiple Choice Options

  • A third
  • B fourth
  • C second
  • D first

Step-by-Step Verified Solution

mBD × mAD = − 1

⇒  (3−24−0)×(b−0a−0)=−1

⇒  b + 4a = 0      . . . . (i)

JEE Main 2019 (Online) 10th January Evening Slot Mathematics - Straight Lines and Pair of Straight Lines Question 108 English Explanation
mAB × mCF = − 1

⇒  ((b−2)a−0)×(34)=−1

⇒  3b − 6 = − 4a

⇒  4a + 3b = 6      . . . . .(ii)

From (i) and (ii)

a = −34, b = 3

∴  IInd quadrant.

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