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6th Edition

Daniel C. Alexander + 1 other

Publisher: Cengage Learning

ISBN: 9781285195698

Chapter 7.CT, Problem 1CT

Textbook Problem

Draw and describe the locus of points in the plane that are equidistant from parallel lines *l *and *m.*

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Expert Solution

To determine

**To draw and describe:**

The locus of points in the plane that are equidistant from parallel lines *l *and *m.*

**Solution:**

The locus is in between both lines and is parallel to both.

**Definition:**

A locus is set of all points and only those points that satisfy a given condition or set of conditions.

In 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:**

A locus maintains an equal distance from each line.

Thus, we obtain that the locus must be half way between the two lines. In addition, since it maintains a constant distance, it must be parallel to both.

From this we came to know that the locus equidistant from two parallel lines *l* and *m*, is a line parallel to both *l* and *m *and halfway between them.

**Conclusion:**

The path formed by all points the same distance from two parallel lines will be one line halfway between the parallel lines.

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Elementary Geometry for College Students

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