In the step shown of the construction of a line through a point that is perpendicular to the given
line, why must the compass point be placed on points a and b? how would the construction be
different if the compass point were placed at random points on the original line?

I think that it would not be in the middle in you did not put the compass on the points A and B.  

Step-by-step explanation:

The compass point must be placed on points A and B because you need to make arcs which would allow you to make the perpendicular line through the given line. The construction would be different if the compass point were placed at random points on the original line because then the line would not be lined up correctly in the middle and it will not be correct, hence why you need to put the compass on A and B.

Step-by-step explanation: This is what I said for my answer on edg

1) c 2143.6 cm

2) c 113.0 m

3) a 33.5 ft

4)   d 2 cm

5) c 20 mm

6) 180 in

7) d 120 ft