Question

which illustration shows the markings for the construction of the perpendicular bisector of $overline{xy}$?

Explanation:

Step1: Recall perpendicular - bisector construction

To construct the perpendicular bisector of a line segment $\overline{XY}$, we first set the compass width to more than half the length of $\overline{XY}$. Then, with the compass centered at $X$, we draw arcs above and below the line segment. Next, with the same compass width and centered at $Y$, we draw arcs above and below the line segment that intersect the previous arcs. The line joining the intersection - points of these arcs is the perpendicular bisector of $\overline{XY}$.

Step2: Analyze each option

In option B, we see arcs drawn from both $X$ and $Y$ (above and below the line segment $\overline{XY}$) and the intersection - points of these arcs which are used to construct the perpendicular bisector. Option A has incorrect arc - placements. Option C has arcs that do not correspond to the construction of the perpendicular bisector of $\overline{XY}$. Option D has only one set of arcs from one endpoint.

Answer:

B.