Question

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

(from unit 1, lesson 3.)

Explanation:

Step1: Construct perpendicular bisector

Use a compass. Place the compass at point A, set the width to more than half the distance between A and B. Draw arcs above and below the line segment AB. Then, without changing the compass width, place the compass at point B and draw similar arcs. The two pairs of arcs intersect at two points. Draw a line through these two intersection - points. This is the perpendicular bisector of segment AB.

Step2: Identify mid - point

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

Step3: Form new segment

The line segment AM (or BM) is half the length of segment AB.

Answer:

Construct the perpendicular bisector of segment AB to find its mid - point. The line segment from either A or B to the mid - point is half the length of segment AB.