How to constrain Polyline to draw only orthogonal lines

Hi All,

I have a collection of points in the same plane that I'd like to draw a Polyline through. The caveat is that I'm trying to to connect these points only with orthogonal lines. See image below:

Result of polyline command (undesired result):

What i'm trying to do (orthogonal lines):

Currently trying to solve this by drawing orthogonal lines through each existing point. Then solving the intersection of those orthogonal lines. Then drawing a polyline through new and existing points. No success yet. Anybody have a better way?