Justin is constructing a line through point q that is perpendicular to line n. he has already constructed the arcs shown. a line n and an arc with center q is drawn. center q lies above the line n. the arc cuts the line on two points a and b. a is left of b. another arc is made with a center at a. the arc cut the line segment a b near point b. the arc is symmetric to line a b. he places his compass on point b to construct an arc. what must be true about the width of the compass opening when justin draws the arc?

I believe that this problem has the following choices:

It must be equal to BQ .
It must be wider than when he constructed the arc centered at point A.
It must be equal to AB .
It must be the same as when he constructed the arc centered at point A.

The correct answer is the last one:

It must be the same as when he constructed the arc centered at point A.

The compass must be the same width as it was when he constructed the arc from point A.

Step-by-step explanation:

In order to construct a perpendicular line to a given line, we need to construct a point above and a point below the line such that the segment through them meets the line at a right angle.

When he constructed the arc from point A, it gave him one piece to creating these points.  An arc from point B, intersecting the arc from point A at two points, will give him the two points he needs.

In order for the arc from point B to intersect the arc from point A, however, the width of the compass must be the same as it was when he constructed the arc from point A.