   Chapter 7.1, Problem 34E ### Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698

#### Solutions

Chapter
Section ### Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698
Textbook Problem
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# In Exercises 27 to 34, 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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