Question

15,625 Learners found this answer helpful

here are 2 points in the plane. explain how to construct a line segment that is half the length of segment ab.

Explanation:

Step1: Construct perpendicular bisector

Use a compass. Place the compass at point A, set a radius greater than half of the distance between A and B, and draw arcs above and below the line - segment AB. Repeat the same process with the compass at point B. The two pairs of arcs will intersect at two points. Draw a line through these two intersection points. This is the perpendicular bisector of AB.

Step2: Locate mid - point

The point where the perpendicular bisector intersects AB is the mid - point M of AB.

Step3: Construct another perpendicular bisector

Let's say we want to find a line - segment half of AB starting from A. Place the compass at M, set a radius equal to AM, and draw an arc that intersects the perpendicular bisector at a point (say N).

Step4: Determine the new line - segment

The line - segment AN (or any line - segment with one endpoint at A and the other on the perpendicular bisector at a distance equal to AM) is half the length of AB.

Answer:

Use a compass and straight - edge to first construct the perpendicular bisector of line segment AB to find its mid - point. Then, using the mid - point and compass, construct a line segment with one endpoint at A (or B) and length equal to half of AB.