Question

how can you find the midpoint of a segment using a compass?
to find the midpoint of a segment, open the compass to about $\frac{1}{3}$ the length of the line segment. place the compass on one of the endpoints and draw an arc above and below the segment. switch to the other endpoint and draw an arc above and below. using a straightedge, draw a line through the two points of intersection of the arcs.
to find the midpoint of a segment, open the compass to exactly $\frac{2}{3}$ the length of the line segment. place the compass on one of the endpoints and draw an arc. where this arc intersects the line segment is where the midpoint of the segment is located.
to find the midpoint of a segment, open the compass to exactly $\frac{1}{2}$ the length of the line segment. place the compass on one of the endpoints and draw an arc. where this arc intersects the line segment is where the midpoint of the segment is located.
to find the midpoint of a segment, open the compass to about $\frac{2}{3}$ the length of the line segment. place the compass on one of the endpoints and draw an arc above and below the segment. switch to the other endpoint and draw an arc above and below. using a straightedge, draw a line through the two points of intersection of the arcs.

Explanation:

The correct way to find the mid - point of a segment with a compass is to open the compass to more than half the length of the line segment. Place the compass on one endpoint and draw arcs above and below the segment. Then do the same from the other endpoint. The line through the intersection points of these arcs bisects the original segment. The first and fourth options describe this correct process. The second and third options are incorrect as setting the compass to $\frac{2}{3}$ or $\frac{1}{2}$ of the segment length and just drawing an arc from one endpoint won't necessarily find the mid - point.

Answer:

To find the midpoint of a segment, open the compass to about $\frac{1}{2}$ the length of the line segment (more precisely, more than half). Place the compass on one of the endpoints and draw an arc above and below the segment. Switch to the other endpoint and draw an arc above and below. Using a straightedge, draw a line through the two points of intersection of the arcs. So the correct options are the first and fourth statements in the original list.