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..

Point E is closer to point A

Step-by-step explanation:

"I have added screenshot of the complete question as well as the

diagram"

- In this diagram, line segment CD is the  perpendicular bisector of line

 segment  AB

∴ AB ⊥ CD

∵ CD intersect AB at M

∴ M is the mid-point of AB

∴ The length of  AM = the length of MB

- Assume the conjecture that the set of  points equidistant from A

 and B is the  perpendicular bisector of AB is true

∴ Any point lies on the line CD equidistant from A and B

- If point E lies on the line CD

∵ CD is the perpendicular bisector of AB

∵ E lies on CD

∴ The length of EA = The length of EB

- From the figure point E is on the left side of the line CD

∵ Point A is on the left side of the line CD

∵ Point B is on the right side of the line CD

∵ Point E is on the left side of the line CD

∴ The length of AE < The length of BE

∴ Point E is closer to point A

a. -0.3 > -0.33