Dear Brandon:

One solution to your problem appears on p282 of M.Gardner's Time Travel. This is one of the problems on which J.J.Sylvester spent his last years, not just three days. Number 9 points:

123
456
789

Now stretch the upper and bottom rows symmetrically so that points 368, 148, 269, and 247 form four lines. Other six: 123,456,789,258,357,159.

Best regards,
Alexander Bogomolny