Centroids and Orthocenters

Centroid
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?
Orthocenter
Tell whether the orthocenter is [i]inside[/i], [i]on[/i], or [i]outside[/i] 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?
Real world
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.
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Information: Centroids and Orthocenters