Use the midpoint formulas to find the midpoints of segments and .
and
where and are the coordinates of the segment end points.
Use the two-point form of an equation of a line to write an equation of a line that passes through vertex and the midpoint of segment . Simplify as you like.
Use the two-point form of an equation of a line to write an equation of a line that passes through vertex and the midpoint of segment . Simplify as you like.
Two-point form:
where and are the coordinates of the given points.
Once you have derived both equations, solve the 2X2 independent and consistent system. The solution set will be the centroid.
If you are a glutton for punishment, you can check your work by writing an equation of a line that passes through vertex and the midpoint of segment . Then pair this new equation with either of the other two and solve the new 2X2 system. Given error-free work, you get the same solution set to the system.
John
My calculator said it, I believe it, that settles it
