Chapter 17: Co-ordinate Geometry

Example 5. Prove that coordinates of the centroid of a triangle ABC, with vertices (x₁ y₁), (x₂, y₂) and (x₃, y₃) are given by

Solution:-

Let the vertices of triangles be A(x₁, y₁), B(x₂, y₂) and C(x₃, y₃)

Let D be the mid-point of BC.

Co-ordinates of D are

Let centroid of triangle ABC be G.

Co-ordinates of G are

Example 6. Find the value of m for which the points with co-ordinates (3, 5), (m, 6) and (1/2, 15/2) are collinear.

Solution :- Let the three points be A (3, 5) B (m, 6) and (1/2, 15,2)

As points A, B and care collinear