For what values of 'x' and 'y' will the points (0,0), (3,root3) and (x,y) form an equilateral triangle?

Answer 1

This is a bit tough to type here, so I'll explain the process rather than giving the answer directly.

First, find the distance between the two given points using the co-ordinate distance formula.

Using the same distance formula, taking (0,0) as one point and (x,y) as the other, and equating it to the distance you obtained above, you'll get an equation in x and y

If you repeat this for (3,root3) and (x,y), you will get another such equation

Solve the two equations to get two values each of x and y.