Concept explainers
Calculate the number of points on line l that are the same distance from point A as from point B.
Answer to Problem 52STP
There may be two cases it may have all points or may have no points.
Explanation of Solution
Given:
It is given in the question that there is a line l which is perpendicular to a segment AB at E.
Let’s sketch the line l and the segment AB.
For the point P to be the same distance from point A and point B, the line l should bisect the segment AB, thus, AE = EB.
Since l was drawn as a perpendicular at a random point AB, then it don’t know anything about the lengths of the segments AE, EB.
So, the answer would be
(i) If l is a perpendicular bisector of AB, then all points on l are at equal distance from A and B.
(ii) If l is not perpendicular bisector of AB, then no points on l are at equal distance from A and B.
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Geometry, Student Edition
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