gen-define-the-centroid-of-a-triangle-and-give-one-short-worked-2175

Define the centroid of a triangle and give one short worked example.

# Centroid of a Triangle ## Definition The **centroid** of a triangle is the point where the three medians intersect. A median is a line segment connecting a vertex to the midpoint of the opposite side. The centroid is located **2/3 of the distance** from each vertex along its median. ## Coordinate Formula For a triangle with vertices at $(x_1, y_1)$, $(x_2, y_2)$, and $(x_3, y_3)$, the centroid is at: $$G = \left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right)$$ ## Worked Example Find the centroid of a triangle with vertices at $A(2, 3)$, $B(6, 5)$, and $C(4, 9)$. **Solution:** $$G = \left(\frac{2 + 6 + 4}{3}, \frac{3 + 5 + 9}{3}\right)$$ $$G = \left(\frac{12}{3}, \frac{17}{3}\right)$$ $$G = \left(4, \frac{17}{3}\right) = (4, 5.67)$$ The centroid is located at $(4, 5\frac{2}{3})$.