Question

select the correct answer from the drop - down menu. using only a compass and a straightedge, you are constructing a line perpendicular to \\( \overline { a b } \\) and passing through a given point, \\( m \\) on \\( \overline { a b } \\). with a compass of set width, you have drawn arcs that intersect \\( \overline { a b } \\) on each side of \\( m \\) and marked the two intersection points as \\( p \\) and. the next step in this construction is to place the compass needle on

Explanation:

Step1: Recall perpendicular - line construction steps

When constructing a perpendicular line to a line segment \(\overline{AB}\) through a point \(M\) on \(\overline{AB}\):

1. First, with a compass of set width, draw arcs that intersect \(\overline{AB}\) on each side of \(M\) and mark the intersection points as \(P\) and \(Q\).
2. The next step is to use the compass to create arcs above and below the line \(\overline{AB}\) to find the points for the perpendicular line. To do this, we need to place the compass needle on \(P\) (or \(Q\)) and set the compass width to a length that will allow us to draw arcs above and below \(\overline{AB}\). The width should be set beyond \(M\) (so that when we draw arcs from \(P\) and then from \(Q\) (with the same width), the arcs will intersect above and below \(\overline{AB}\)).

Answer:

P and set its width beyond M