Question

question 2 of 39
joaquin is constructing the perpendicular bisector of \\( \overline { a b } \\). what should be his
first step?
a. open his compass so that the distance from the two points of the
compass is less than half the length of \\( \overline { a b } \\).
b. open his compass so that the distance from the two points of the
compass is half the length of \\( \overline { a b } \\).
c. open his compass so that the distance from the two points of the
compass is one quarter the length of \\( \overline { a b } \\).
d. open his compass so that the distance from the two points of the
compass is wider than half the length of \\( \overline { a b } \\).

Explanation:

Step1: Recall perpendicular bisector construction steps

To construct the perpendicular bisector of a line segment \( \overline{AB} \), we first need to create two arcs (one from point \( A \) and one from point \( B \)) that intersect above and below the segment.

Step2: Determine compass width

If the compass width is less than half the length of \( \overline{AB} \) (options A and B), the arcs from \( A \) and \( B \) will not intersect. If the compass width is one - quarter the length of \( \overline{AB} \) (option C), the arcs will also not intersect. Only when the compass is opened wider than half the length of \( \overline{AB} \) (option D) can we create intersecting arcs from \( A \) and \( B \), which is the first step in constructing the perpendicular bisector.

Answer:

D. Open his compass so that the distance from the two points of the compass is wider than half the length of \( \overline{AB} \).