Final answer:
To double the length of a given segment using a compass, measure the segment with the compass, draw a longer line, and create two arcs intersecting that line from segment's ends. Connecting the intersections will provide the desired segment length.
Step-by-step explanation:
To construct a segment that is twice the length of a given segment using a compass, one appropriate method is to first use the compass to measure the length of the original segment. After that, you will draw a line longer than the given segment. Place the compass point on one end of the segment and swing an arc with the compass width set to the length of the segment. Without changing the width of the compass, move the compass point to the intersection of the first arc and the drawn line. From this new point, swing another arc that crosses the line. The total length from the original endpoint of the segment through the two arc intersections is now twice the length of the original segment. This corresponds with the procedure outlined in option a: Draw two circles with the compass, connecting their intersections for the desired length.