Medians and Centroid
Medians meet at the centroid, 2/3 along each.
Key idea
Medians meet at the centroid, 2/3 along each.
In depth
A median joins a vertex to the midpoint of the opposite side. The three medians meet at the centroid, which divides each in ratio 2 : 1 from the vertex. It is the centre of mass.
Worked example
For vertices (0,0), (6,0), (0,6): centroid = ((0+6+0)/3, (0+0+6)/3) = (2, 2).
Real-world uses
- Finding the balance point of a triangular sheet of metal or a shelf bracket
Common mistake
Thinking the centroid splits medians 1 : 1.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Medians and Centroid?
Medians meet at the centroid, 2/3 along each. It is a topic at the advanced level in Geometry.
Where is Medians and Centroid used in real life?
Real-world examples: Finding the balance point of a triangular sheet of metal or a shelf bracket.
What should I learn before Medians and Centroid?
Make sure you are comfortable with Angle Bisector Theorem, the previous topic in Geometry.
What is a common mistake with Medians and Centroid?
Thinking the centroid splits medians 1 : 1.
How can I practise Medians and Centroid?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Medians and Centroid?
Move on to Circumcentre and Incentre next.
Related advanced topics in Geometry
- Heron’s Formula – Triangle area from three sides.
- Regular Polygon Area – Use apothem and perimeter.
- Arc Length of a Circle – Part of the circumference.
- Sector Area – Part of the circle’s area.
- Central and Inscribed Angles – An inscribed angle is half the central angle on the same arc.
- Chord and Tangent Properties – A tangent is perpendicular to the radius at the point of contact.