Question

geometry
show work
name_
review: constructions m1 - t1
date_ phase_
construct a line segment the given number of times longer than the given segment.

1. 5 times as long
2. 3 times as long

a) construct the perpendicular bisector of each. b) label the intersection as point c.
3)
4)
construct a line segment the given number of times longer than the given segment.

1. 3 times as long

Explanation:

Step1: Constructing longer line - segment (for 1, 2, 5)

Use a straight - edge and compass. For a line segment \(AB\) to be \(n\) times as long, first draw a ray starting from one end of the original segment. Then, using the compass, mark off \(n\) equal lengths along the ray equal to the length of the original segment.

Step2: Constructing perpendicular bisector (for 3, 4a)

Place the compass at one end of the line segment, open it more than half the length of the segment. Draw arcs above and below the segment. Repeat from the other end of the segment. The line joining the intersection points of these arcs is the perpendicular bisector.

Step3: Labeling intersection (for 3, 4b)

After constructing the perpendicular bisector, mark the point where the bisector intersects the original line segment as point \(C\).

Since this is a geometric construction problem, the actual construction cannot be fully shown in text - based format. But the steps for performing the required geometric operations are described above.

Answer:

Follow the above - described construction steps for each part of the problem. For the construction of longer line segments, use the ray and compass method. For perpendicular bisectors, use the arc - intersection method and then label the intersection as required.