Question

which of the following is the correct construction for a perpendicular bisector?

Explanation:

Step1: Recall the construction of a perpendicular bisector

To construct a perpendicular bisector of a line segment \(AB\), we first draw arcs with the same radius from points \(A\) and \(B\) above and below the line segment \(AB\).

Step2: Analyze each option

• In the first option, there are not enough arcs (only one arc above and one arc below with incorrect centers in a sense of the full - construction).
• In the second option, the arcs are not drawn correctly (the lower arc is only a semi - arc and the upper arcs are not symmetric in a full - construction sense).
• In the third option, we have arcs drawn from both \(A\) and \(B\) with the same radius above and below the line segment \(AB\). The intersection points of these arcs are used to draw the perpendicular bisector.
• In the fourth option, the arcs are drawn in a non - standard way (the arcs seem to be tangent at the mid - point instead of intersecting at two distinct points above and two distinct points below for a proper construction).

Answer:

The third option (the one with arcs drawn from both \(A\) and \(B\) above and below the line segment \(AB\) and intersecting at four points) is the correct construction for a perpendicular bisector.