A median is a line segment connecting a vertex of a triangle to the midpoint of the opposite side. Every triangle has exactly three medians, and they all intersect at a single point called the Centroid. The Median of Triangle Calculator takes your vertex coordinates and computes the precise length of each median instantly.
Features
Coordinate Input: Works with any set of 3 (x,y) vertices.
Tri-Median Handling: Calculates $m_a, m_b,$ and $m_c$ simultaneously.
Visual Representation: Draws dashed lines representing the medians on a coordinate grid.
Precision: Outputs lengths up to 3 decimal places.
How to Use This Calculator
Enter Points: Input the X and Y coordinates for vertices A, B, and C.
Calculate: Click the button to process the midpoints and distances.
Read Results: Identify the length of the median originating from each specific vertex.
Visualize: Use the diagram to see how the lines cross at the center.
Formulas
The calculator uses the following mathematical principles:
Midpoint Formula: $$ M = (\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}) $$
Distance Formula: $$ d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2} $$
Apollonius Theorem: Alternate method relating side lengths to median length.
Practical Applications
Physics: Finding the center of mass (Centroid) relies on median intersection.
Structural Engineering: Designing braces that connect to the midpoint of beams.
Land Surveying: Subdividing triangular plots into equal areas (a median divides a triangle’s area in half).
Tips for Success
Area Property: Each median splits the triangle into two smaller triangles of equal area.
Intersection: The point where they cross (Centroid) is always 2/3 of the way along the median from the vertex.
Input Order: Does not matter; the logic applies to the shape regardless of winding order.
Frequently Asked Questions (FAQ)
What is the difference between an altitude and a median?
An altitude is perpendicular to the opposite side (height). A median connects to the midpoint of the opposite side.
Are the medians always equal?
Only in an equilateral triangle. In an isosceles triangle, two are equal.
Final Words
Split the difference with precision. The Median of Triangle Calculator is the essential tool for geometers and engineers needing to find the exact bisecting lines of any triangular shape.
