sub solve{
    my( $a, $b, $c, $d ) = @_;
    my( $x, $y );

    $x = ($b - $a) / ($d - $a - $c + $b);
    $y = ($d - $a) * ($b - $a) / ($d - $a - $c + $b) + $a;
    
    return( $x, $y );
}
[download]

sub solve{
    my( $a, $b, $c, $d ) = @_;

    my $x = ($b - $a) / ($d - $a - $c + $b);
    my $y = ($d - $a) * $x + $a;
    
    return( $x, $y );
}
[download]

formula for line 1:   Y = (D - A) * X + A
formula for line 2:   Y = (C - B) * X + B

intersection: X and Y coordinates of line1 and line2 are equal ...

(D - A) * X + A = (C - B) * X + B

reduces to =>  X = (B - A) / (D - A - C + B)

plug X into equation for line 1 gives ...

Y = (D - A) * (B - A) / (D - A - C + B) + A
[download]