Concept explainers
Find the locus of all the points in the plane of two parallel lines s and t , equidistant from s and t , and 4 cm from a particular point A in the plane .
Answer to Problem 5ST3
Two points , one point or no point.
Explanation of Solution
Calculation:
The locus of all the points in plane of two parallel lines s and t is the line parallel to both and in between s and t :
The locus of all the points in plane that are 4 cm from point A in the plane is
So, the locus of all the points in the plane of two parallel lines s and t , equidistant from s and t , and 4 cm from a particular point A in the plane will be intersection of above two cases.
So, it can be two points , one point , or no point , depending on various cases of location of A and distance between the lines s and t.
For example:
If distance between the lines s and t is 8 cm.
Case I: A lie on any lines s or t .
The locus of all the points in the plane of two parallel lines s and t , equidistant from s and t , and 4 cm from a particular point A in the plane is one point .
Case II: A is in between lines s and t .
The locus of all the points in the plane of two parallel lines s and t , equidistant from s and t , and 4 cm from a particular point A in the plane are two points .
Case III: A is neither in between nor on lines s and t .
The locus of all the points in the plane of two parallel lines s and t , equidistant from s and t , and 4 cm from a particular point A in the plane is no point .
Chapter 10 Solutions
McDougal Littell Jurgensen Geometry: Student Edition Geometry
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