Elementary Geometry for College Students (7th Edition) Clone

Published by Cengage
ISBN 10: 978-1-337-61408-5
ISBN 13: 978-1-33761-408-5

Chapter 7 - Review Exercises - Page 348: 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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