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The othocenter of DeltaABC with vertices...

The othocenter of `DeltaABC` with vertices `B(1,-2)` and `C(-2,0)` is `H(3,-1)`.Find the vertex A.

Text Solution

Verified by Experts

The correct Answer is:
`(3//7,-34//7)`
Let the coordinates of vertex A be (x,y).
`AHbotBC`
or `("Slope of" AH)xx("Slope of" BC) =1`
or `(y+1)/(x-3)xx(-2-0)/(1-(-2)=-1`
or `3x-2y=11`
Also, `BHbotAC`
or `("Slope of" BH)xx("Slope of" AC)=1`
or `(-2-(-1))/(1-3)xx(y-0)/(x-(-2))=-1`
or `-y=2x+4`
or `2x+y=-4`
Solving (1) and (2) , we get
`x=(3)/(7),y=-(34)/(7)`
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