Is it possible to scale unidirectionally?

[JohnLay]

I am attempting to align school floorplans with the building footprint. Unfortunately for me, the floorplans do not appear to be to scale. The Scale Geometry feature scales proportionately in all directions. I only need to do it in one. See example.

[DanPatterson]

Do the floor plans have a defined projected coordinate system?

If so, you should add it to an empty map (no basemap and definitely not the image) since it will set the base coordinate system.  Once added, then add the image.  If it has a coordinate system, it should project on the fly to match that of the vector layer.

I suspect that the image may be in a web mercator coordinate system.

Don't assess the need to stretch the vector layer until you can ensure that both layers have a know coordinate system, that can be projected to a common coordinate system, one that minimize distortions (aka, web mercator)