Concept explainers
To draw and describe:
The locus of points in the plane that are equidistant from parallel lines l and m.
Answer to Problem 1CT
Solution:
The locus is in between both lines and is parallel to both.
Explanation of Solution
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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Chapter 7 Solutions
Elementary Geometry For College Students, 7e
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