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If a vertex of an equilateral triangle is the origin and the side opposite to it has the equation x+y=1, then orthocentre of the triangle is :

Text Solution

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`ax+by+c=0`
`(x1,y1)`
`(x-x1)/a=(y-y1)/b=-(ax1+by1+c)/(a^2+b^2)`
`x/1=y/1=-(-1)/(1^2+1^2)`
`x=1/2,y=1/2`
`G=(((2xx1/2+1xx0)/(2+1),2xx1/2+1xx0)/(2+1))`
`G=(1/3,1/3)`
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