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Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

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BuyFindarrow_forward

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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