Offsetting multiple points

I have a multiline shapefile and a point shapefile. The points are supposed to fall in the center of line breaks but when imported to qgis, the points fall on one end of a line break. Is there a method to center these points? There is way to many to offset individually or selecting several points and using ‘move feature’ tool.

Here is what QGIS looks like and what the CAD drawing looks like. Im on QGIS 3.10.14