   Chapter 7.1, Problem 34E 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 three noncollinear points D , E , and F .

To determine

To find:

The locus of points that are equidistant from three non-collinear points D, E, and F.

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:

Let O be a point on a plane. The line OY is perpendicular to the plane.

The points D, E and F are the non-collinear points. That means all the three points do not lie on a straight line.

If all the points are projected, then we obtain a point Y

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