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# Ratios of directed line segments calculator

To find coordinates or ratios of directed line segments enter values in input box to use this Partitioning a line segment calculator(Divide line segments/Partition calculator).

Table of Contents:

## Formula

**Section or Ratio Externally**

(mx2-nx1/m-n , my2-ny1/m-n)

**Section or Ratio Internally**

(mx2+nx1/m+n , my2+ny1/m+n)

Coordinates of Points Calculator finds the dividing line segments (ratios of directed line segments). It finds the coordinates using partitioning a line segment. The Coordinates of points is determined a pair of numbers defining the position of a point that defines its exact location on a two-dimensional plane.

Using partition calculator - Ratio formula or section formula is used to find the coordinates of a point P which divides the segment joining the points A and B internally or externally in the ratio m:n.

Case 1: **Find the coordinates of the point which divides the line joining the points (2, 3), (4, 5) internally in the ratio 2:1.**

x1 = 2, y1 = 3 and

x2 = 4, y2 = 5

m = 2, n = 1

**Apply Formula**

(mx2+nx1/m+n , my2+ny1/m+n)

(2*4+1*2/2+1 , 2*5+1*3/2+1)

(8+2/3 , 10+3/3 )

(10/3 , 13/3)

**(3.3 , 4.3)**

Case 2: **Find the coordinates of the point which divides the line joining the points (2, 1), (3, 4) externally in the ratio 2:5.**

x1 = 2, y1 = 1 and

x2 = 3, y2 = 4

m = 2, n = 5

**Apply formula**

(mx2-nx1/m-n , my2-ny1/m-n)

(2*3-5*2/2-5 , 2*4-5*1/2-5)

(6-10/-3 , 8-5/-3)

(-4/-3 , 3/-3)

**(4/3 , -1)**

**References: **

- Partitioning a Segment in a Given Ratio. Varsitytutors.com.
- Slope to Partition Segments by study.com
- Roberts, D. Directed Line Segments - MathBitsNotebook(Geo - CCSS Math).
- Points on the coordinate plane (article) | Khan Academy.
- Coordinates of Points by mathopenref.com
- Directed Line Segment Worksheet by teachers.stjohns.k12.fl.us