   Chapter 7.1, Problem 17E 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 the midpoints of all chords of a circle Q that are parallel to diameter P R - .

To determine

To find:

The locus of the midpoints of all chords of a circle Q that are parallel to diameter PR-.

Explanation

Approach:

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: Construct a circle any radius by taking the diameter as PR-.

Step 2: Draw a line (shown in red) AB- perpendicular to the PR- through the center of the circle. The locus of the midpoints of all chords of a circle Q that are parallel to diameter PR- lie on the line AB

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