Question

what is the first step in constructing the perpendicular bisector of $overline{ab}$? a use your straightedge to draw a line through the intersections of the arcs. b place the point of the compass at point b and draw an arc between points a and b. c place the point of the compass at point a and draw an arc between points a and b. d place the point of the compass at point b and open the compass so that it is greater than half of the distance from point b to point a.

Explanation:

Step1: Recall perpendicular - bisector construction

To construct the perpendicular bisector of a line segment $\overline{AB}$, the first step is to set the compass width to be greater than half of the length of $\overline{AB}$. We can start by placing the point of the compass at either point $A$ or point $B$.

Step2: Analyze options

Option A is the last step. Option B and C do not set the compass width correctly. Option D correctly describes the first - step of placing the point of the compass at one of the endpoints (in this case point $B$) and opening the compass to be greater than half of the distance between the two endpoints.

Answer:

D. Place the point of the compass at point B and open the compass so that it is greater than half of the distance from point B to point A.