Find Circumcenter, Orthocenter and Centroid Algebraically

Master the algebraic methods for finding the three key points of concurrency in a triangle: the circumcenter, orthocenter, and centroid! In this comprehensive tutorial, Mario's Math Tutoring guides you through the definitions, formulas, and step-by-step techniques for each. You'll learn: Centroid: Where the medians intersect, how to find the midpoint of a side, and the easy average formula for its coordinates. Circumcenter: The intersection of perpendicular bisectors, how to calculate perpendicular slopes, midpoints, and solve systems of equations to find its location. Orthocenter: Where the altitudes cross, how to determine perpendicular slopes from vertices to opposite sides, and set up equations for their intersection. We'll work through two detailed examples, applying these concepts to specific triangle vertices. Plus, gain a deeper understanding with visual diagrams illustrating where each center lies in acute, right, and obtuse triangles. This video is perfect for geometry students looking to solidify their understanding of triangle centers and their algebraic calculations! Timestamps: 0:00 - Introduction: Finding Circumcenter, Orthocenter, Centroid Algebraically 0:30 - What is a Centroid? (Medians & Point of Concurrency) 0:50 - Centroid Formula: Average of Coordinates 1:20 - Example 1: Calculating the Centroid 1:50 - What is a Circumcenter? (Perpendicular Bisectors) 2:20 - Finding Perpendicular Slope & Midpoint (for AC) 3:00 - Equation of Perpendicular Bisector (for AC) 3:25 - Finding Perpendicular Slope & Midpoint (for AB) 4:00 - Equation of Perpendicular Bisector (for AB) 4:25 - Solving System of Equations to Find Circumcenter 6:20 - What is an Orthocenter? (Altitudes) 6:50 - Equation of Altitude from C to AB 7:35 - Equation of Altitude from B to AC 8:00 - Solving System of Equations to Find Orthocenter 9:10 - Visualizing Circumcenter Locations (Acute, Right, Obtuse Triangles) 11:40 - Visualizing Orthocenter Locations (Acute, Right, Obtuse Triangles) 13:50 - Visualizing Centroid Locations (Always Inside) 15:30 - Example 2: Finding Centroid, Circumcenter, Orthocenter 15:50 - Calculating Centroid for Example 2 16:50 - Calculating Circumcenter for Example 2 (Perp. Bisector AC) 18:00 - Calculating Circumcenter for Example 2 (Perp. Bisector AB) 19:20 - Solving for Circumcenter in Example 2 21:20 - Calculating Orthocenter for Example 2 (Altitude to AC) 22:30 - Calculating Orthocenter for Example 2 (Altitude to AB) 23:25 - Solving for Orthocenter in Example 2 25:00 - Conclusion and More Practice ➡️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