Chapter 12.6, Problem 52STP

To determine

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.