Question

1. in this diagram, line segment cd is the perpendicular bisector of line segment ab. assume the conjecture that the set of points equidistant from a and b is the perpendicular bisector of ab is true. is point e closer to point a, closer to point b, or the same distance between the points? explain how you know. ab ⊥ cd

Explanation:

Step1: Recall the property of perpendicular bisector

The set of points equidistant from \(A\) and \(B\) is the perpendicular bisector of \(AB\).

Step2: Check the position of point \(E\)

Point \(E\) is not on the perpendicular bisector \(CD\) of \(AB\). Points on the perpendicular bisector of a line - segment are equidistant from the endpoints of the line - segment. Since \(E\) is not on \(CD\), it is not equidistant from \(A\) and \(B\). And by visual inspection or the property of perpendicular bisector, \(E\) is closer to \(A\) than to \(B\).

Answer:

Point \(E\) is closer to point \(A\).