   Chapter 7.1, Problem 33E 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 the midpoints of the radii of a sphere whose center is point O and whose radius has a length of 5 m.

To determine

To find:

The locus of points that are the midpoints of the radii of a sphere whose center is point O and whose radius has a length of 5 m.

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:

Step 1: Take appropriate scale and construct a circle of radius equivalent to 5 m (In two dimensional space, the sphere is drawn as a circle) with O as center. The distance OA=5 m.

Step 2: Locate the point B such that it divides the length OA as shown in figure.

Step 3: Draw a circle (dashed and red in colour) with O as center and OB as radius

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