Question

If the points $(4,-4),(-4,4)$ and $(x,y)$ from an equilateral triangle, find $x$ and $y$.

Answer 1

$\therefore$for ABC to be equilateral $\Delta$

$AB=BC=CA$

$\therefore$ By distance formula

$AB=\sqrt{(4-(-4){)}^2+(-4-4{)}^2}=8\sqrt{2}BC=\sqrt{(x+4{)}^2+(y-4{)}^2}CA=\sqrt{(x-4{)}^2+(y+4{)}^2}\therefore A{B}^2=B{C}^2=C{A}^2(x+y{)}^2+(y+4{)}^2=128\to \left(1\right)\&(x-4{)}^2+(y+4{)}^2=128\to \left(2\right)$

Solving the equations $\left(1\right)\&\left(2\right)$

$x=y=4\sqrt{3}$