* The centroid is the point of intersection of all 3 medians of a triangle. It can be determined by finding the equations of two of the median lines, and the finding the point of intersection of those two lines using elimiation or substitution.
Steps to Find the Equation of a Median
1. Find the midpoint of one line segment, using the midpoint formula. Remember: You should indicate which midpoint you are finding by writing the letter coordinates of the end points of the line segment. ie) MAB
2. Find the slope of the median line (Remember: use the coordinates of the midpoint and the vertex opposite the midpoint.)
3. Now that you have the slope, substitute in either the coordinates of the midpoint or the coordinates of the vertex, as well as the slope, into the y=mx+b formula to find the y-intercept (b).
4. Finish off by writing y=mx+b one more time, replacing m with the slope of the median, and b with the y-intercept.
You now have the equation of the median.
Practice Questions
Page 174 #13.
Page 195 #8, 12, 17a, 24.
