Find coordinates of vertex of equilateral triangle

Question

$ABC$ is an equilateral triangle , $AC = 2 $

What is the value of $p$ and $q$ ?

Answer 1

HINT:

So, $C$ has to be $(2,0)$

Now, equating the squares of lengths of the sides $$(p-0)^2+(q-0)^2=(p-2)^2+(q-0)^2$$

Solve for $p$ and find $q$ from $p^2+q^2=2^2$

Answer 2

By symmetry, $p=1$. Then use Pythagoras to get $q$ from $2^2=1^2+q^2$