Video Transcript
Where does the center of gravity of a uniform triangular lamina lie?
Letβs firstly consider the scaling triangle π΄π΅πΆ as shown. If π΄ has coordinates π₯ one, π¦ one; π΅ has coordinates π₯ two, π¦ two; and πΆ has coordinates π₯ three, π¦ three. We know that the center of gravity lies at the point π₯ one plus π₯ two plus π₯ three divided by three, π¦ one plus π¦ two plus π¦ three divided by three. This point occurs at the intersection of the medians.
The median from vertex π΄ bisects the line π΅πΆ. Likewise, the median from π΅ bisects the line π΄πΆ. Finally, the median from πΆ bisects the line π΄π΅. The intersection of these three lines is the center of gravity of a uniform triangular lamina.
