Question

to write the equatuinn of the line which is the perpendicular bisector of a segment: what coordinates willl you use? what slope will you use?

Answer 1

If you know the slope of the line segment (call it m), then the slope of a line perpendicular to the line segment is -1/m (flip m, and negate it).
If you know a point on the bisector, then you can use the point, slope formula to find teh equation of the bisector.