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  • Help me please, 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?

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?

  • Option 1)

    first

  • Option 2)

    fourth

  • Option 3)

    second

  • Option 4)

    third

Answers (1)

best_answer

 

Orthocentre -

The point of intersection of the altitude of a triangle.

- wherein

 

From the concept we have learnt 

m_{BD}\times m_{AD}=-1

=>(\frac{3-2}{4-0})\times (\frac{b-0}{a-0})=-1

=>4a+b=0....................................(1)

m_{AB}\times m_{CF}=-1

=>(\frac{b-2}{a-0})\times (\frac{3-0}{4-0})=-1

=>4a+3b=6................................(2)

`from (1) and (2)

a=\frac{-3}{4},b=3

\therefore IInd quadrant


Option 1)

first

Option 2)

fourth

Option 3)

second

Option 4)

third

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