Hello, hm_498!

I'll give you a small start . . .

Find the centroid, circumcenter, and the orthocenter of the triangle with vertices:

. .

I must assume you are familiar with slopes and equations of lines . . .

Thecentroidis the intersection of themedians.

A median joins a vertex to the midpoint of the opposite side.

First, find some of the midpoints of the sides.

Let be the midpoint of side . .Then:

. . Write the equation of , the line through and

Let be the midpoint of side . .Then:

. . Write the equation of , the line through and

The centroid is the intersection of and .

Hints for the rest of the problem:

Thecircumcenteris the intersection of theperpendicular bisectorsof the sides.

Theorthocenteris the intersection of thealtitudesto the sides.