   Chapter 7.1, Problem 11E 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 at a given distance from a fixed line.

To determine

To find:

The locus of points that are at a given distance from a fixed line.

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:

To find the locus of points that are at a given distance from a fixed line, we follow the below procedure.

Step 1: Construct an arbitrary line (which is red in colour) from any point. Let it be reference line.

Step 2: Draw line (which is blue in colour) at any distance from the reference line.

Step 3: Draw another line (which is black in colour) by taking the same distance as that the previous one on the other side of the reference line as shown in the figure...

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