Ratios of directed line segments calculator

Partition calculator 

Ratios of directed line segments calculator is an online tool that finds the point coordinates dividing the line (internally/externally) joining two points A and B for a given ratio m and n.

Coordinates of a point - Definition

Coordinates of a point are a pair of numbers that state its precise location on a two-dimensional plane. The coordinate plane has two axes at right angles to each other, called the x and y axis.

Formula of coordinates dividing a line segment

Coordinates dividing line internally

Coordinates dividing line externally

Where,

x₁, x₂, y₁, y₂ are end point of a line segment,

m and n are external and internal ratios.

How to find ratio of a directed line segment?

Let’s find out coordinates of points dividing a line segment joining two points with an example.

Example:

Find the point coordinates that divides a directed line segment internally having endpoints (2, 4), (3, 6) with a ratio of 5:6.

Solution:

Step 1: Identify the values.

x₁ = 2, x₂ = 3, y₁ = 4, y₂ = 6, m = 3, n = 1

Step 2: Place the values in equation of internal ratio of directed line segment.

= (mx₂+nx₁/m+n, my₂+ny₁/m+n)

= (3×3+1×2/3+1, 3×6+1×4/3+1)

= (11/4, 22/4)

Hence, the points (11/4, 22/4) divides the line joining points (2, 4), (3, 6) with a ratio of 5:6.

Use external ratio segment formula for external points coordinates or use our segment partition calculator above to automate your calculations.