Calculate the intersection of two lines

Y =  X + 
Y =  X + 
Intersection of two lines：

What is the Intersection of Two Lines?

The intersection of two lines is the point where they meet or cross in a 2D or 3D space.

  • In 2D, two non-parallel lines always intersect at a single point.
  • In 3D, two lines may not intersect unless they are coplanar (lie on the same plane).

Why Calculate the Intersection of Two Lines?

  • Geometry & Mathematics: Solving linear equations.
  • Physics & Engineering: Finding collision points, signal paths, or structural intersections.
  • Computer Graphics: Used in ray tracing and object rendering.
  • Navigation & Mapping: GPS applications and traffic modeling.

How to Calculate the Intersection?

For two lines in 2D:

Given Two Lines in General Form:

The intersection point (x,y)is found using:

Given Two Lines in Slope-Intercept Form (y=mx+b)

If two lines are:

Set them equal to each other:

Solving for x:

Then plug x back into one equation to find y.

When to Use Intersection Calculation?

  • Physics & Motion Tracking: Predicting object collisions.
  • Game Development: Detecting object interactions.
  • Machine Learning & AI: Path optimization in robotics.
  • Navigation & Traffic Systems: Analyzing road intersections.