Quadrants · Superchallenge problem

A point in Quadrant II is farther from the $x$-axis than from the $y$-axis. It is reflected across the $x$-axis, across the $y$-axis, and across both axes one after the other. The original point and its three images are the corners of a rectangle with perimeter $36$ units and area $80$ square units. What is the sum of the coordinates of the original point?