Question

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 two endpoints \(A\) and \(B\) is the perpendicular bisector of the line - segment \(AB\). Point \(E\) is not on the perpendicular bisector \(CD\) of \(AB\).

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

Since point \(E\) is on the side of the perpendicular bisector closer to \(A\), by the property that points on one - side of the perpendicular bisector of a line segment are closer to one of the endpoints, point \(E\) is closer to point \(A\).

Answer:

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