Question

If the points $(1,1)(-1,-1)$ and $(-\sqrt{3},k)$ are vertices of an equilateral triangle, Find the value of $k$

Answer 1

$A(1,1),B(-1,-1)$ and $C(\sqrt{3},k)$ are vertices of equilateral triangle

AB=BC=CA=>$(AB{)}^2=(AC{)}^2$

=>$=>2{(1+1)}^2=(1+\sqrt{3}{)}^2+(1-k{)}^2=>3=-2k+k^2=>k^2-2k-3=0k=3,-1$