For example, if one side of the triangle is 10 cm long, the midpoint will be at 5 cm, since 10/2=5{\displaystyle 10/2=5}.
For example, if the side of the triangle is 12 cm long, the midpoint will be at 6 cm, since 12/2=6{\displaystyle 12/2=6}.
A vertex is the point at which two sides of a triangle meet.
The center of gravity is where the three medians intersect, but since the medians only intersect in one point, you can use a shortcut and find the center of gravity by only finding the intersection of two medians.
For example, you might have a median that is 3. 6 cm long.
For example, if your median is 3. 6 cm long, you would divide 3. 6 by 3:3. 6cm/3=1. 2cm{\displaystyle 3. 6cm/3=1. 2cm}, so ⅓ of the median is 1. 2 cm.
For example, on a median that is 3. 6 cm long, the centroid will be 1. 2 cm up from the midpoint.
For example, you might be given triangle PQR, and you need to find and label point P (3, 5), point Q (4, 1), and R (1, 0).
For example, if your three x-coordinates are 3, 4, and 1, add these three values together: 3+4+1=8{\displaystyle 3+4+1=8}.
For example, if your three y-coordinates are 5, 1, and 0, add these three values together: 5+1+0=6{\displaystyle 5+1+0=6}.
For example, if the sum of your x-coordinates is 8, the average x-coordinate is 8/3{\displaystyle 8/3}. If the sum of your y-coordinates is 6, the average y-coordinate is 6/3{\displaystyle 6/3}, or 2{\displaystyle 2}.
In the example problem, the center of gravity is the point (8/3,2){\displaystyle (8/3,2)}.
