The centroid of a triangle is the point of intersection of the 3 medians of the triangle.
A median of a triangle is the line that goes from one vertex to the midpoint of the opposite side of the triangle.
*** In the attached image, lines BE, CF, and AD are the medians & point G is the centroid. ***
The formula to calculate the centroid of a triangle is:
[tex](x,y)=(\frac{x_{1}+x_{2}+x_{3}}{3}),(\frac{y_{1}+y_{2}+y_{3}}{3})[/tex]
Where,
- [tex](x,y)[/tex] are the coordinates of the centroid
- [tex](x_{1},y_{1}),(x_{2},y_{2}), AND (x_{3},y_{3})[/tex] are the 3 vertices of the triangle
Using the 3 points [tex]P(-4,-1), Q(2,2), R(2,-3)[/tex] and substituting in the formula gives us:
[tex](x,y)=(\frac{-4+2+2}{3},\frac{-1+2+(-3)}{3})\\(x,y)=(\frac{0}{3},\frac{-2}{3})\\(x,y)=(0,-\frac{2}{3})[/tex]
ANSWER: Coordinate of the Centroid of the Triangle [tex](0,-\frac{2}{3})[/tex]
