   Chapter 7.1, Problem 36E Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Solutions

Chapter
Section Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem

Note: Exercises preceded by an asterisk are of a more challenging nature.In Exercises 29 to 36, Sketch and describe the locus of points in space.Find the locus of points that are equidistant from all points on the surface of a sphere with center point Q .

To determine

To find:

The locus of points that are equidistant from all points on the surface of a sphere with center point Q.

Explanation

Definition:

A locus is set of all points and only those points that satisfy a given set of conditions.

It must be noted that, the phrase “all points and only those points” has dual meaning as follows:

1. All points of the locus satisfy the given condition.

2. All points satisfying the given locus conditions are included in the locus.

Calculation:

We need to find the locus of points that are equidistant from all points on the surface of a sphere with center point Q.

Draw a circle with center Q as shown in the two dimensional figure. From the figure, we find that the locus of points that are equidistant from all points on the surface of a sphere with center point Q is the surface of the sphere

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