Question

joaquin is constructing the perpendicular bisector of $overline{ab}$. he opens his compass so that the distance from the two points of the compass is wider than half the length of $overline{ab}$. what is his next step?
a. place the point of the compass on point a and draw an arc across $overline{ab}$.
b. place the point of the compass on point a and mark where the arc intersects $overline{ab}$.
c. place the point of the compass on the midpoint of $overline{ab}$ and draw an arc in either direction.
d. place the point of the compass on the midpoint of $overline{ab}$ and mark the points directly above and below the midpoint.

Explanation:

To construct a perpendicular bisector of $\overline{AB}$, after setting the compass width wider than half of $\overline{AB}$, the next step is to anchor the compass at one endpoint of the segment and draw arcs that extend above and below the segment (the option describes this as drawing an arc across $\overline{AB}$, which aligns with the standard first arc-drawing step from endpoint A). The other options are incorrect because using the midpoint is not possible yet (we are constructing the bisector to find the midpoint), and marking intersections on $\overline{AB}$ is not the correct initial action.

Answer:

A. Place the point of the compass on point A and draw an arc across $\overline{AB}$.