**Introduction to section formula help:**

In mathematics, section formula is related to the coordinate geometry. This section formula helps to divide the line in two ways such as internally or externally. By applying the section formula, we can easily find the point which can bisects the given line. This article helps to give the section formula and some example problems using that section formula.

Consider a line with two end points A(x1, y1) and B(x2, y2).

There are two types of section formula depends on the point P(x,y) which divides the given line AB.

**Section formula for internal division:**

`((mx_2+nx_1)/(m+n), (my_2+ny_1)/(m+n))`

**Representation of section formula for internal division:**

**Section formula for external division:**

`((mx_2-nx_1)/(m-n),(my_2-ny_1)/(m-n))`

**Representation of section formula for external division:**

**Example: 1**

Determine the coordinate of the point P(x,y) which divides the line of points (2, 2) and (2, 5) internally in the ratio of 1 :2.

**Solution:**

Given:

(x_{1}, y_{1}) = (2, 2)

(x_{2}, y_{2}) = (2, 5 )

m : n = 1 : 2

**Step 1:**

**Section formula for internal division:**

`((mx_2+nx_1)/(m+n), (my_2+ny_1)/(m+n))`

**Step 2:**

`(mx_2+nx_1)/(m+n)` = `(1 xx 2+2xx2)/(1+2)`

= `(2 + 4)/3`

= `6/3`

= 2

**Step 3:**

`(my_2+ny_1)/(m+n)` = `(1xx5+2xx2)/(1+2)`

= `(5+4)/3`

= `9/3`

= 3

**Answer:** P(x, y) = (2, 3)

**Example: 2**

Determine the coordinate of the point P(x,y) which divides the line of points (5, 2) and (6, 3) internally in the ratio of 3 :2.

**Solution:**

Given:

(x_{1}, y_{1}) = (5, 2)

(x_{2}, y_{2}) = (6, 3)

m : n = 3 : 2

**Step 1:**

**Section formula for external division:**

`((mx_2-nx_1)/(m-n),(my_2-ny_1)/(m-n))`

**Step 2:**

`(mx_2-nx_1)/(m-n)` = `(3xx6-2xx5)/(3-2)`

= `(18-10)/1`

= 8

**Step 3:**

`(my_2-ny_1)/(m-n)` = `(3xx3-2xx2)/(3-2)`

= `(9-4)/1`

= 5

**Answer:** P(x, y) = (8, 5)

**Problem: 1**

Determine the coordinate of the point P(x,y) which divides the line of points (6, 3) and (2, 5) internally in the ratio of 2 :4.

**Answer:** P(x, y) = (5, 3)

**Problem: 2**

Determine the coordinate of the point P(x,y) which divides the line of points (5, 3) and (7, 6) internally in the ratio of 3 :2.

**Answer:** P(x, y) = (11, 12)