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.
Want to see more full solutions like this?
Chapter 7 Solutions
Elementary Geometry For College Students, 7e
- Elementary Geometry for College StudentsGeometryISBN:9781285195698Author:Daniel C. Alexander, Geralyn M. KoeberleinPublisher:Cengage LearningElementary Geometry For College Students, 7eGeometryISBN:9781337614085Author:Alexander, Daniel C.; Koeberlein, Geralyn M.Publisher:Cengage,Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage
- Algebra: Structure And Method, Book 1AlgebraISBN:9780395977224Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. ColePublisher:McDougal LittellLinear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage LearningGlencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill