QuestionWhat is the first step to construct the perpendicular bisector of segment $\overline{AB}$ if it's already drawn? A. Draw an arc with compass at $A$ greater than $\frac{1}{2} AB$ . B. Draw an arc with compass at $A$ of length $\frac{1}{4} AB$ . C. Draw an arc with compass at $A$ of length $\frac{1}{2} AB$ . D. Draw an arc with compass at $A$ less than $\frac{1}{2} AB$ .

Studdy Solution

STEP 1

Assumptions1. We have a straight line segment $\overline{\mathrm{AB}}$ . . We have a compass and a straightedge for construction.
3. We are constructing the perpendicular bisector of $\overline{\mathrm{AB}}$ .

STEP 2

To construct the perpendicular bisector, we need to draw two arcs, one centered at point $A$ and the other at point $B$ . The radius of these arcs should be more than half the length of $\overline{\mathrm{AB}}$ so that they intersect above and below the line segment.
Thus, the correct first step is to put the compass point on point $A$ and draw a long arc. Be sure the opening is greater than $\frac{1}{2} A B$ . This corresponds to option A.

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