Problem

Construct the perpendicular bisector of \(AB\) using \(\text{one}~\text{compass}~\text{radius}\) greater than \(AB/2\). State the arc centers and intersections, the line to draw, and the perpendicular-bisector result.

Big Picture

What this problem is really about

The arcs are not decorative; their shared radius encodes equal distances from both segment endpoints. We’ll first ensure the radius is large enough to create two crossings, then use those two equidistant points as a locus argument that determines a single line and its relationship to the original segment.

Answer choices

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Preview only

radius = greater than AB/2; centers = midpoint; intersections = P,Q; joining line = PQ; result = perpendicular bisector

radius = different radii from A and B; centers = A,B; intersections = join any points; joining line = join intersections; result = perpendicular bisector

radius = same compass radius greater than AB/2; centers = A and B; intersections = P,Q; joining line = draw PQ; result = PQ is perpendicular to AB and bisects AB

radius = equal; centers = A,B; intersections = P,Q not yet located; joining line = draw PQ first; result = perpendicular bisector

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Construct the perpendicular bisector of \(AB\) using \(\text{one}~\text{compass}~\text{radius}\) greater than \(AB/2\). State the arc centers and intersections, the line to draw, and the perpendicular-bisector result.

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