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Two vertices of a triangle are (5,-1) an...

Two vertices of a triangle are `(5,-1)` and `(-2,3)` If the orthocentre of the triangle is the origin, find the coordinates of the third point.

Text Solution

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Let the coordinates of third vertex be `C(a,b)`.

Since, `CH` is`botAB`,
`:. ((b)/(a))((4)/(-7))=-1`
`implies4b=7a` ….....`(i)`
Also, `AHbotBC`
`:. (-(1)/(5))((3-b)/(-2-a))=-1`
`implies3-b=-10-5a` .......`(ii)`
On solving Eqs. `(i)` and `(ii)` , we get
`a=-4`, `b=-7`
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