Section Formula

The section formula is a formula in coordinate geometry that is used to find the coordinates of a point that divides a line segment in a given ratio. The formula is as follows:

If P is the midpoint of AB, then it divides AB in ratio k : 1, so its coordinates are 

.

Mid-Point Formula

If P is the midpoint of AB, then it divides AB in a ratio of 1:1, so its coordinates are 

Note: This formula is also called as mid-point formula.

Example 1: Find the coordinates of the point which divides the line segment joining the points (6, 3) and (-4, 5) in the ratio 3 : 2 internally.

Solution:

Let us assume a point P (x, y) which divides the line segment joining the points (6, 3) and (−4, 5) in the ratio 3 : 2 internally.

Here, m = 3, n = 2, x₁ = 6, y₁ = 3, x₂ = −4 and y₂ = 5.

Substitute all the above values in section formula.

Therefore, the coordinates of P are (0, 21/5).

Example 2: In what ratio does point C (3/5, 11/5) divide the line segment joining points A (3, 5) and B (−3, −2)?

Solution:

Let us assume the point C divide AB in the ratio λ : 1.

Here, x₁ = 3, y₁ = 5, x₂ = −3 and y₂ = −2

The coordinates of C is given by (3/5, 11/5)

⇒ 3(k + 1) = 5(−3k+3)

⇒ 3k + 3 = −15k + 15

⇒ 18k = 12

⇒ k = 2/3

⇒ 11(k + 1) = 5 (−2k+5)

⇒ 11k + 11 = −10k + 25

⇒ 21k = 14

⇒ k = 2/3

Hence, the point C divides AB in the ratio 2 : 3.

Example 3: The three vertices of a parallelogram taken in order are (−1, 0), (3, 1) and (2, 2) respectively. Find the coordinates of the fourth vertex.

Solution:

Let the fourth vertex be D (x, y).

Since, the diagonals of a parallelogram bisect each other.

Mid-point of AC = Mid-point of BD

Compare the coordinates.

3 + x = 1 ⇒x = −2

(y + 1)/ 2=1

y + 1 = 2

y = 1

Hence, the fourth vertex of parallelogram is (−2, 1).

CBSE Class 10 Maths Notes Chapter 7 Coordinate Geometry are provided to support student’s education. We believe that students’ learning and development are of the utmost importance, and that’s why we have created these comprehensive notes to help them comprehend the complex subject of Coordinate Geometry better.

The NCERT Class 10 Maths textbook’s Chapter 7 explores the realm of Coordinate Geometry and covers various concepts such as distance formula, section formula, and more. Our notes aim to provide students with a complete summary of the entire chapter, including all essential topics, formulae, and concepts necessary to succeed in their exams.