Is the red line parallel to an axis (i.e., x or y)? If so, select the one that is in the correct position, and set the cursor to it. Next, with the cursor as the pivot point, select the other vert and scale to 0 (zero): press S Shift-x 0 (zero), and enter (or S Shift-y).
Edit: Was on break at work for the above. At home, I tried the same method except using the coordinates set to normal, and it worked as well with any orientation to the global axes. So just find the axis between the verts, and use Shift- to exclude that axis from the scaling operation.
Edit 2: Since videos are getting all the attention, I thought I would re-propose my solution which requires no add-ons nor extra geometry. It goes fast so feel free to pause to read the shortcuts used: