Concept explainers
(a)
Find the locus of points in Z and equidistant from R and S.
(a)
Answer to Problem 10CT
All the points on the perpendicular bisector of the line segment joining R and S.
Explanation of Solution
Given:
R and S are points in a plane Z.
Calculation:
Observe:
The points shown can be generalised :
All the points on the perpendicular bisector of the line segment RS are equidistant from both points R and S.
Also, we can check any other point from outside the perpendicular bisector of the line segment RS will not be equidistant from R and S.
So, the locus of points in Z and equidistant from R and S is the perpendicular bisector to the line segment joining R and S.
(b)
Find the locus of points in space and equidistant from R and S.
(b)
Answer to Problem 10CT
All the points on the perpendicular bisectors in the space, of the line segment joining R and S.
Explanation of Solution
Given:
R and S are points in a plane Z.
Calculation:
Similar to part (a) , if we extend it,
All the points on the perpendicular bisector of the line segment RS are equidistant from both points R and S, the perpendicular bisector can be in space.
So, the locus of points in space and equidistant from R and S are the perpendicular bisectors in space , to the line segment joining R and S.
Chapter 10 Solutions
McDougal Littell Jurgensen Geometry: Student Edition Geometry
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