   Chapter 7.1, Problem 15E 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 11 to 22, sketch and describe each locus in the plane.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 noncollinear points D, E and F.

Explanation

Definition:

The locus of points in a plane that are equidistant from the endpoints of a line segment is the perpendicular bisector of that line segment.

Calculation:

Step 1: Locate any arbitrary point G. Let this be the fixed point or reference point.

Step 2: Locate three points D, E and F at an equal distance from the fixed point G.

Step 3: Join them by a straight line (shown in black). The distance between the fixed point and the three collinear points D, E and F is same. Or in other words, DG=EG=FG

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