Question

Line CD is the perpendicular bisector of segment AB. The lines intersect

at point E. Which of these statements is true?
(Hint: it may help to draw a picture, but you don't have to turn it in!)
There is not enough information to be sure.
O E is closer to A than to B.
O E is closer to B than to A.
O E is the same distance from A and B.
plz help me understand this

Answer 1

E is the same distance from A and B. ⇒ D

Explanation:

Let us explain the meaning of perpendicular bisector

If line m is the perpendicular bisector of line n, then

• line m intersect line n at the mid-point of line n

• They form 4 right angles around this mid-point

∵ Line CD is the perpendicular bisector of segment AB

∴ Line CD intersects segment AB at the mid-point of AB

∵ Line CD and segment AB intersected at point E

→ That means E ∈ CD and E ∈ AB

∴ Point E is the mid-point of line AB

∴ Point E divides line AB into 2 equal parts

→ That means point E is at the same distance from points A and B

∴ E is the same distance from A and B.