Where does the center of gravity of a uniform triangular lamina lie?
Let’s firstly consider the scaling triangle 𝐴𝐵𝐶 as shown. If 𝐴 has coordinates 𝑥 one, 𝑦 one; 𝐵 has coordinates 𝑥 two, 𝑦 two; and 𝐶 has coordinates 𝑥 three, 𝑦 three. We know that the center of gravity lies at the point 𝑥 one plus 𝑥 two plus 𝑥 three divided by three, 𝑦 one plus 𝑦 two plus 𝑦 three divided by three. This point occurs at the intersection of the medians.
The median from vertex 𝐴 bisects the line 𝐵𝐶. Likewise, the median from 𝐵 bisects the line 𝐴𝐶. Finally, the median from 𝐶 bisects the line 𝐴𝐵. The intersection of these three lines is the center of gravity of a uniform triangular lamina.