Centroid of a Triangle
Centroid of a triangle is the point of intersection of all three medians of a triangle. The centroid of a triangle having its vertices A(x1,y1), B(x2,y2), and C(x3,y3) is given by the formula
Centroid (x,y) = {(x1+x2+x3) / 3, (y1+y2+y3) / 3}
Example: Find the centroid of the triangle whose vertices are A(2, 7), B(3, -1), and C(-5, 6).
Solution:
Let A(2, 7), B(3, -1) and C(-5, 6) be the vertices of the given △ABC.
(x1 = 2, y1 = 7), (x2 = 3, y2 = -1) and (x3 = -5, y3 = 6).
Centroid (x,y) = {(x1+x2+x3) / 3 , (y1+y2+y3) / 3}
= {2+3+(-5)}/3 , {7+(-1)+6}/3
= (0 , 12)
Coordinate Geometry
Coordinate geometry is the branch of mathematics that deals with plotting the curve on the coordinate axes. Various curves can be plotted on the coordinate plane using coordinate geometry formulas. Co-ordinate geometry uses algebraic equations to plot various curves on the coordinate plane. One of the popular coordinate systems used in mathematics is the rectangular Cartesian system.
Table of Content
- What is Coordinate Geometry?
- Coordinates of a Point
- Distance Formula
- Mid-Point Formula
- Section Formula
- Slope Formula
- Area of Triangle
- Condition for Collinearity of Three Points
- Centroid of a Triangle