Centroids and Orthocenters

Point D is the centroid of the triangle and the length of each median is given. What is the distance between point D and each of the other points? How did yow find the measurements?

Tell whether the orthocenter is inside, on, or outside the triangle. Then find the coordinates of the orthocenter. The vertices of the triangle are L(0, 5), M(3, 1), N(8, 1).

Define the criteria needed for a triangle to have an orthocenter on the triangle itself.

Define the criteria needed for a triangle to have an orthocenter outside the triangle itself.

Define the criteria needed for a triangle to have an orthocenter inside the triangle itself.

When is the orthocenter of a triangle found at the same point as the centroid?

You're making a triangular mobile to decorate your room. You want to be sure that it balances properly and hangs well. Describe at least two methods to ensure that it is balanced.