Question

If $(-4,3)$ and $(4,3)$ are two vertices of an equilateral triangle, find the co-ordinates of the third vertex.

Answer 1

Let find out $A(x,y)$

$BC=\sqrt{(-4-4{)}^2+(3-3{)}^2}=8$

In equilateral triangle .

$AB=BC=\sqrt{(x+4{)}^2+(y-3{)}^2}=8$ .....(i)

$AC=BC=\sqrt{(x-4{)}^2+(y-3{)}^2}=8$ .....(ii)

from (i) and (ii) we get,

$x=0,y=4\sqrt{3}+3$

$A(0,4\sqrt{3}+3)$