SOLUTION: Please help. I am homeschooled and i don't understand how to find loci. Can you help me sketch and ddescribe all points in a plane that are equidistant from the vertices of triangl

It is not a locus, it is but one point.

There is but one point which is equidistant from the three vertices of a
triangle, and that point is called the circumcenter. Here is a 
demonstration of the circumcenter.

We start with this triangle:



I claim that the point marked O is the one and only
point which is equally distance from the three vertices:



And if we draw a circle with the circumcenter as the center, going
through any one of the vertices, it will go through all three vertices:




The line segments drawn from it to the three vertices,



are all equal in length because they are radii of the same circle.

Want to see how to construct the circumcenter of a triangle?

Go here:

http://www.mathopenref.com/constcircumcenter.html

Edwin