> For the complete documentation index, see [llms.txt](https://trizen.gitbook.io/sidef-lang/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://trizen.gitbook.io/sidef-lang/programming_tasks/f/find_the_intersection_of_two_lines.md).

# Find the intersection of two lines

```ruby
func det(a, b, c, d) { a*d - b*c }
 
func intersection(ax, ay, bx, by,
                  cx, cy, dx, dy) {
 
    var detAB = det(ax,ay, bx,by)
    var detCD = det(cx,cy, dx,dy)
 
    var ΔxAB = (ax - bx)
    var ΔyAB = (ay - by)
    var ΔxCD = (cx - dx)
    var ΔyCD = (cy - dy)
 
    var x_numerator = det(detAB, ΔxAB, detCD, ΔxCD)
    var y_numerator = det(detAB, ΔyAB, detCD, ΔyCD)
    var denominator = det( ΔxAB, ΔyAB,  ΔxCD, ΔyCD)
 
    denominator == 0 && return 'lines are parallel'
    [x_numerator / denominator, y_numerator / denominator]
}
 
say ('Intersection point: ', intersection(4,0, 6,10, 0,3, 10,7))
say ('Intersection point: ', intersection(4,0, 6,10, 0,3, 10,7.1))
say ('Intersection point: ', intersection(0,0, 1,1, 1,2, 4,5))
```

#### Output:

```
Intersection point: [5, 5]
Intersection point: [2300/459, 2320/459]
Intersection point: lines are parallel
```


---

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