Question

all the points equidistant from the given two points A and B lie on the __________ of the line segment AB​

Answer 1

PERPENDICULAR BISECTOR

Step-by-step explanation:

all the points equidistant from the given two points A and B lie on the PERPENDICULAR BISECTOR  of the line segment AB​

Proof :

Let say AB is the line Segment

XY is the perpendicular Bisector interesecting AB at  O

=> AO = BO  

∠AOX = ∠AOY  = ∠BOX = ∠BOY = 90°

Lets  take  any point P on XY

Comparing Δ AOP  & ΔBOP

AO = BO

∠AOP = ∠BOP = 90°

OP = OP  ( common)

=> Δ AOP  ≅ ΔBOP

=> AP = BP

Hence all the points equidistant from the given two points A and B lie on the perpendicular bisector of the line segment AB​

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Answer 2

Answer:

Perpendicular bisector