In physics and engineering, the balance point is everything. The Centroid of Triangle Calculator finds this center of mass (often denoted as G). By taking the coordinates of the three vertices, this tool calculates the exact point where the triangle would perfectly balance on a pin.
Features
Coordinate Geometry: Uses the (x, y) coordinates of the three vertices.
Center of Mass: Calculates the average of x-values and y-values.
Visual Plot: Graphs the triangle and its Centroid on a cartesian plane.
Median Visualization: Draws the medians (lines from vertex to midpoint) intersecting at the centroid.
How to Use This Calculator
Enter Coordinates: Input $(x_1, y_1)$, $(x_2, y_2)$, and $(x_3, y_3)$.
Calculate: Press the button to generate the Centroid (G).
View: See the graph showing the intersection of the medians.
Verify: Read the step-by-step arithmetic (average calculation).
Formulas
The calculator uses the following mathematical principles:
Centroid Formula: $$ G(x, y) = \left( \frac{x_1+x_2+x_3}{3}, \frac{y_1+y_2+y_3}{3} \right) $$
Midpoint Formula: $$ M = \left( \frac{x_1+x_2}{2}, \frac{y_1+y_2}{2} \right) $$
Practical Applications
Engineering: Finding the center of gravity for triangular plates or supports.
Computer Graphics: Calculating the center of polygons for rotation or mesh processing.
Map Analysis: Finding the geographic center of a triangular region defined by 3 cities.
Tips for Success
Always Inside: The centroid is always located *inside* the triangle.
Medians: It is the point where the three medians (lines from vertex to opposite midpoint) intersect.
2:1 Ratio: The centroid divides each median in a 2:1 ratio.
Frequently Asked Questions (FAQ)
What is a median?
A line segment joining a vertex to the midpoint of the opposing side.
Does it work for negative coordinates?
Yes, standard Cartesian math applies regardless of quadrants.
Final Words
Find the perfect balance. The Centroid of Triangle Calculator makes finding the geometric center of any triangle effortless and visibly clear.
