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

Using a compass, with center at point A and radius greater than half of the distance between A and B, draw arcs above and below the line segment AB. Repeat the same process with center at point B and the same radius. 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, which divides AB into two equal parts.

Step2: Select half - length segment

Let the perpendicular bisector intersect AB at point M. The line segment AM (or BM) is half the length of segment AB.

Answer:

Construct the perpendicular bisector of segment AB using a compass and straight - edge. The segment from either A or B to the mid - point (where the perpendicular bisector intersects AB) is half the length of segment AB.