Centroid of a TriangleThe point at which the medians of a triangle intersect is called the centroid of the triangle.
Let ABC be a given triangle with vertices A(x1, y1), B(x2, y2) and C(x3, y3).Since D is the mid-point of BC, its coordinates are [(x2 + x3)/2, (y2 + y3)/2]
Let G(x, y) be a point dividing AD in the ratio 2:1.
Similarly, the coordinates of a point which divides BE in the ratio 2:1 as well as those of the point which divides CF in the ratio 2:1 are
Incentre of a Triangle
The point at which the bisectors of the angles of a triangle intersect, is called the in-centre of the triangle. From geometry, we know that the bisector of an angle of a triangle divides the opposite side in the ratio of length of remaining sides. Hence, the bisectors of the angle of âABC are concurrent, and meet at a point, called In-centre.
Area of TriangleLet ABC be a given triangle whose vertices are A(x1, y1), B(x2, y2) and C(x3, y3).
Area of the triangle
If we interchange the order of any two vertices of the DABC, we obtain a negative value of the area. However, the area shall always be taken to be positive.