I found the necessary module on CPAN. It's called Imager::Graph::Util. Here's an example script:

#!/usr/bin/perl -w
use strict;
use Imager::Graph::Util;

my ($ax, $ay, $bx, $by, $cx, $cy, $dx, $dy) = GetLines(); # you have t
+o write that subroutine

my @line1 = line_from_points($ax, $ay, $bx, $by);
my @line2 = line_from_points($cx, $cy, $dx, $dy);

# @p will contain the (x, y) point of intersection if it exists
my @p = intersect_lines(@line1, @line2);
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