Assume AB¯¯¯¯¯¯¯¯
has already been constructed. To construct the perpendicular bisector of AB¯¯¯¯¯¯¯¯
, first put the compass point on point A and draw a long arc. Is there a maximum distance for the compass setting at this step? Explain.(1 point)
Responses
Yes, the compass setting must be less than one half the length of AB¯¯¯¯¯¯¯¯
. If the setting were greater, the arcs at each endpoint would not intersect. If the setting were less than one half the length of AB¯¯¯¯¯¯¯¯
, the arcs would intersect only once at the midpoint of AB¯¯¯¯¯¯¯¯
.
Yes, the compass setting must be less than one half the length of line segment cap A cap b. If the setting were greater, the arcs at each endpoint would not intersect. If the setting were less than one half the length of line segment cap A cap b, the arcs would intersect only once at the midpoint of line segment cap A cap b.
Yes, the compass setting must be less than one half the length of AB¯¯¯¯¯¯¯¯
. If the setting were greater, the arcs would intersect only once at the midpoint of AB¯¯¯¯¯¯¯¯
. If the setting were exactly one half the length of AB¯¯¯¯¯¯¯¯
, the arcs centered at each endpoint would not intersect.
Yes, the compass setting must be less than one half the length of line segment cap A cap b. If the setting were greater, the arcs would intersect only once at the midpoint of line segment cap A cap b. If the setting were exactly one half the length of line segment cap A cap b, the arcs centered at each endpoint would not intersect.
No, for any compass setting greater than one half the length of AB¯¯¯¯¯¯¯¯
, the arcs would intersect in one point above the segment.
No, for any compass setting greater than one half the length of line segment cap A cap b, the arcs would intersect in one point above the segment.
No, for any compass setting greater than one half the length of AB¯¯¯¯¯¯¯¯
, the arcs would intersect in two places, one above and one below the segment.
Yes, the correct response is:
Yes, the compass setting must be less than one half the length of AB¯¯¯¯¯¯¯¯. If the setting were greater, the arcs at each endpoint would not intersect. If the setting were less than one half the length of AB¯¯¯¯¯¯¯¯, the arcs would intersect only once at the midpoint of AB¯¯¯¯¯¯¯¯.
This is because the perpendicular bisector of a line segment must pass through the midpoint of the segment, and setting the compass to less than half the length ensures that the arcs intersect at this point. If the compass setting is greater than half the length, the arcs will not intersect, and if it is exactly half the length, the arcs may intersect at two points, which would not give the correct perpendicular bisector.