Constructing a Perpendicular Bisector
A perpendicular bisector is a line that crosses a segment at its midpoint and forms a right angle with the segment. To construct it accurately, you need equal-distance points from both endpoints of the segment.
Steps
- Open your compass wider than half the segment. Place the compass point on one endpoint and draw arcs above and below the segment.
- Keep the same compass width. Move the compass point to the other endpoint and draw arcs that intersect the first pair of arcs.
- Mark the intersection points. These two arc intersections are the key construction points.
- Draw a straight line through the intersections. This line is the perpendicular bisector.
Why it works
Every point on the perpendicular bisector is the same distance from both endpoints of the segment. The intersecting arcs create points that are equally far from each endpoint, so the line through them must pass through the midpoint and be perpendicular.
Check your construction
- The line should cross the segment at its midpoint.
- It should form a 90° angle with the segment.
- The two endpoints of the segment should appear symmetrically placed on either side of the bisector.
If asked for a final written answer, give the name or equation of the constructed line in its simplest form.