Point of concurrency △

If two or more lines meet at a single point, the lines are concurrent, and the point at which they meet is called The point of concurrency 

The median of a triangle ( orange lines) are the segments from the vertex of a triangle to the midpoint of the opposite side.

The point of concurrency of the median is called the centroid.




The centroid is important because it divides the median into a 2:1 ratio. The section of the median nearest the vertex is twice as long as the section near the midpoint of the triangle's side.

*If the triangle is obtuse, it is likely for the point of concurrency to fall outside the triangle.


The coordinate of the centroid is the average of the coordinates of the vertices. 

For example: you have triangle a,b,c. a( 0,-6) , b(-10,-6), c(1,0)
so the x of the centroid would be ( 0+ -10 + 1) / 3  = -9/3 = -3.    x=-3
and y would be (-6 + -6+ 0)/3 =-12/3 = -4.  y=-4

therefore, the coordinates would be (-3,-4)


For problems such as : two vertices of a triangle are ( 0,0) and ( 9,0). the centroid is (6,1). Find the third vertex of the triangle.

you would set up the equation as: (0+9+x)/3 =6   so what divided by 3 equals 6? 18. and 9+ 9= 18. so x=9.

for y, (0+0+y)/3= 1 therefore, y must equal 3. because 3 divided by 3 is equal to 1.