There is more than one way to determine what constitutes a line:

use strict;
use warnings;

local $/ = "A red line is found\n";

while (<DATA>) {
  print "Red line $1" if /(at location[^\n]*\n)/;
}

__DATA__
A red line is found
at location 2.5 4.5
A Blue line is found
at location 2.6 4.5
A red line is found
at location 2.67 4.56
The red arc is found
at location 2.5 4.5
[download]

Prints:

Red line at location 2.5 4.5
Red line at location 2.67 4.56
[download]