CENTROID FORMULA PROOF: Centroid is 2/3 the Distance of the Median (Coordinate Geometry)

In this Geometry lesson, you will learn the essential property of the centroid of a triangle: how to prove that the distance from the vertex to the centroid is 2/3 of the entire length of the median. This is a common question in coordinate geometry! We will use the properties of the median and the centroid to set up the problem. A median connects a vertex to the midpoint of the opposite side. The centroid is the point of concurrency where the three medians intersect, also known as the center of mass. Here’s what we cover in this Centroid proof video: Timestamps: 0:00 What is a Centroid and a Median? 0:45 The Centroid Theorem: Proving the 2/3 Median Rule 1:15 How to Find the Centroid using the Centroid Formula (average of coordinates) 2:30 Finding the Midpoint of the opposite side using the Midpoint Formula 3:45 Calculating the total Median Length (CM) using the Distance Formula 4:30 Calculating the distance from the Vertex to Centroid (CP) 5:10 Showing that CP is exactly 2/3 of CM Check out my video on other points of concurrency like the orthocenter and circumcenter! https://youtu.be/_0E0-j-4Xjw?si=9oZRF8Ynx01KOmUx Relevant Topics: #Centroid #Median #CoordinateGeometry #GeometryProof #DistanceFormula #MidpointFormula #MathTutorial ➡️JOIN the channel as a CHANNEL MEMBER at the "ADDITIONAL VIDEOS" level to get access to my math video courses(Algebra 1, Algebra 2/College Algebra, Geometry, PreCalculus), midterm & final exam reviews, ACT and SAT prep videos and more! (Over 390+ videos) https://www.youtube.com/channel/UClOR1BiPyOkkIAnv9Cmj4iw/join