Which point in a triangle is equidistant from the vertices of the triangle? the point of intersection of the altitudes the point of intersection of the medians the point of intersection of the perpendicular bisectors the point of intersection of the angle bisectors

The answer is the point of intersection of the perpendicular bisectors.

There are multiple types of centers for a triangle. The one that is described in the problem is the circumcenter. 

This is found by drawing a perpendicular bisector for each side of the triangle. The point of intersection of these points will be equidistant from each vertice.