Elementary Geometry for College Students (6th Edition)

Published by Brooks Cole
ISBN 10:
ISBN 13:

Chapter 7 - Review Exercises - Page 338: 11

Answer

The locus of the midpoint of a circle is a circle with half of the radius of the initial circle.

Work Step by Step

Recall, a midpoint is the center of the radius, so the midpoint of a radius is equal to half of the radius. In addition, recall that a locus is the curve, line, point, or plane along which the distance from a given point (it can be multiple points, but in this case we are considering the center of the circle) is constant. A constant distance away from the center of the original circle forms another circle. Thus, the locus of the midpoint of a circle is a circle with half of the radius of the initial circle.
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