Algorithm for intersection of 2 lines?

Question

I have 2 lines. Both lines containing their 2 points of X and Y. This means they both have length.

I see 2 formulas, one using determinants and one using normal algebra. Which would be the most efficient to calculate and what does the formula looks like?

I'm having a hard time using matrices in code.

This is what I have so far, can it be more efficient?

public static Vector3 Intersect(Vector3 line1V1, Vector3 line1V2, Vector3 line2V1, Vector3 line2V2) {     //Line1     float A1 = line1V2.Y - line1V1.Y;     float B1 = line1V1.X - line1V2.X;     float C1 = A1*line1V1.X + B1*line1V1.Y;      //Line2     float A2 = line2V2.Y - line2V1.Y;     float B2 = line2V1.X - line2V2.X;     float C2 = A2 * line2V1.X + B2 * line2V1.Y;      float det = A1*B2 - A2*B1;     if (det == 0)     {         return null;//parallel lines     }     else     {         float x = (B2*C1 - B1*C2)/det;         float y = (A1 * C2 - A2 * C1) / det;         return new Vector3(x,y,0);     } } 

Answer 1

Assuming you have two lines of the form Ax + By = C, you can find it pretty easily:

float delta = A1 * B2 - A2 * B1;  if (delta == 0)      throw new ArgumentException("Lines are parallel");  float x = (B2 * C1 - B1 * C2) / delta; float y = (A1 * C2 - A2 * C1) / delta; 

Pulled from here