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 10 - Section 10.6 - The Three-Dimensional Coordinate System - Exercises - Page 491: 42

Answer

(a) The sphere has symmetry with respect to this line. (b) The sphere does not have symmetry with respect to this plane.

Work Step by Step

We can write the general equation of a sphere: $(x-a)^2+(y-b)^2+(z-c)^2 = r^2$ where $(a,b,c)$ is the center of the sphere and $r$ is the radius The equation of the sphere is: $x^2+y^2+z^2 = 100$ The center of the sphere is $(0,0,0)$ (a) A sphere has symmetry with respect to any line that passes through the sphere's center. Since the line passing through the points $(0,0,0)$ and $(0,5,5\sqrt{5})$ passes through the point $(0,0,0)$, the sphere has symmetry with respect to this line. (b) A sphere has symmetry with respect to any plane that includes the sphere's center. Since the plane with the equation $y=5$ does not include the point $(0,0,0)$, the sphere does not have symmetry with respect to this plane.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.