1.

The equation of the base of an equilateral triangle is `x+y=2`and its vertex is `(2,-1)dot`Find the length and equations of its sides.

Answer» `tantheta=|(m_1-m_2)/(1+m_1m_2)|`
`theta=60,m_1=-1,m_2=?`
`tan60=|(-1-m_2)/(1-m_2)|`
`sqrt3=pm(-1-m_2)/(1-m_1)`
`sqrt3-sqrt3m_2=-1-m_2`
`m_2(1-sqrt3)=-1-sqrt3`
`m_2=(-1-sqrt3)/(1-sqrt3)`
`sqrt3-sqrt3m_2=1+m_2`
`m_2(1+sqrt3)=sqrt3-1`
`m_2=(sqrt3-1)/(1+sqrt3)`
`y-y_1=m(x-x_1)`
`y+1=(-1-sqrt3)/(1-sqrt3)(n-2)`
`y+1=(sqrt3+1)/(sqrt3-1)(n-2)`
`y+1=(sqrt3-1)/(sqrt3+1)(n-2)`.


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