Warm Up - Copy each of the following into your notebook, then solve.

Finding the centroid on a coordinate plane Find the coordinates of the centroid of ΔABC if the coordinates of the vertices are located as follows: Here is visual representation of the problem:

We need to find the equations that represent each of the three medians:

Midpoint of BC is: Slope of this median is:

The equation of this line is:

Midpoint of AC is: Slope of this median is:

The equation of this line is:

Midpoint of AB is: Slope of this median is:

The equation of this line is:

Use any two equations and solve for x and y:

Homework: Find the coordinates of the centroid of the triangle with the following vertices:

Warm Up: Find the coordinates of the centroid of the triangle with the following vertices:

Choose any two equations and solve:

Homework: Find the coordinates of the centroid of the triangle with the following vertices:

Altitudes and Orthocenters Construct and label the triangle with the following vertices:

Altitudes and Orthocenters An altitude is a segment that is perpendicular to a side of the triangle and passes thru the opposite vertex. An orthocenter is the point of concurrency of a triangles altitudes

Altitudes and Orthocenters Draw the three altitudes of triangle XYZ. Then approximate the coordinates of the orthocenter

Altitudes and Orthocenters Construct and label the triangle with the following vertices: Draw the three altitudes of triangle DEF. Then approximate the coordinates of the orthocenter

Altitudes and Orthocenters Construct and label the triangle with the following vertices: Draw the three altitudes of triangle DEF. Then approximate the coordinates of the orthocenter

Find the orthocenter of the triangle with the following vertices:

Find the orthocenter of the triangle with the following vertices: