Centroid, Incentre and Circumcentre and Orthocentre of a Triangle - Practice Questions & MCQ

Centroid   

A median is the line joining the mid-points of a side and the opposite vertex of a triangle.

Centroid  of a triangle is the point of intersection of the three medians of the triangle. A centroid divides any median in the ratio 2:1.

The coordinates of the centroid of a triangle (G) whose vertices are A (x₁, y₁), B (x₂, y₂) and C(x₃, y₃), is given by 

Note:

If D (a₁, b₁), E (a₂, b₂) and F (a₃, b₃) are the mid point of ΔABC, then centroid of triangle ABC is given by

Example

If Origin is the centroid of a triangle ABC, and the coordinates of other two vertices of the triangle are  A (4, –3) and B (–5, 2), then find the coordinates of the third vertex.

Solution

Let point C is  (α, β)

Coordinates of C are (1, 1)