SOLUTION: Find the coordinates of the centroid P of triangle ABC.
A(-1,2), B(5,6), C(5,-2)
Algebra.Com
Question 524565: Find the coordinates of the centroid P of triangle ABC.
A(-1,2), B(5,6), C(5,-2)
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
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:
(x\ -\ x_1) )
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
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