Two vertices of an isosceles triangle in the coordinate plane have coordinates (0,0) and (2a,0). where might the third vertex be located?

Since the triangle whose vertices is required is an isosceles triangle, then the third vertex will lie on the perpendicular bisector of the base.

Given that two of the vertices are at point (0, 0) and point (2a, 0), the mid point of the line joining the two given vertices is at point (a, 0).

Therefore, the third vertex of the triangle will lie at point (a, b) where b is any number not equal to 0.