Revision Notes: Section and Mid-Point Formula | Mathematics Class 10 ICSE PDF Download

Co-ordinate geometry is that branch of mathematics which creates geometry algebraically.

The Section Formula

Section formula is used to find the co-ordinates of a point which divides the line segment joining two given points in a given ratio.
If point P divides the line segment joining the points A(x₁, y₁) and B(x₂, y₂), then the coordinates of point P are given by

Mid-Point Formula

Mid-Point formula is used to find the co-ordinates of the mid-point of the line segment joining two given points.
Let P(x, y) be a point lying on a line segment AB, where the coordinates of A and B are (x₁, y₁) and (x₂, y₂) respectively. Suppose P divides AB in the ratio 1 : 1. In other words, P is the mid-point of AB.
⇒ AP = PB
Then coordinates of P are given by

Centroid of a Triangle

The straight line joining the vertex of a triangle to the mid-point of the opposite side is called a median of the triangle.
The point which divides a median of a triangle in the ratio 2 : 1 is called the centroid of the triangle.
Thus, if AD is a median of ΔABC and G is its centroid, then AG/GD = 2/1
Let the vertices of ΔABC are A(x₁, y₁), B(x₂, y₂) and C(x₃, y₃).
Then the coordinate of centroid are given by