Question

PQ is a line segment and line m is a perpendicular bisector if a point A lies on m show that A is equidistant from P and Q ​

Answer 1

Answer:

Given :-

AB is a line segment,

L is drawn perpendicular to AB

A point p lies on line L.

(Also, Shown in figure! Refers to attachment)

To Prove :

• P is equidistant from A and B.

Solution :-

In ∆AOP and ∆BOP ,

OP = OP ( common side )

POA = POB

AO = OB

∆AOP ∆BOP (By S.A.S.)

=> AP = BP ( By C.P.C.T. )

Hence, P is equidistant from A and B .

Thus Proved :)

Answer 2

Given : PQ is a line segment and line m is a perpendicular bisector point A lies on m

To find :  show that A is equidistant from P and Q ​

Solution:

PQ is a line segment and line m is a perpendicular bisector

let say line m intersect PQ at O

PO = OQ    = PQ/2  as  m is bisector

OA ⊥  PQ  as m is perpendicular to PQ &  A is on line m

=> OA ⊥ PO   & OA⊥ QA

in Δ POA

PA² = PO² + OA²

PO = OQ

=> PA² =OQ² + OA²  

in Δ QOA

QA² = QO² + OA²

Equating OQ² + OA²  

=> PA² = QA²

=> PA = QA

QED

Hence proved

A is equidistant from P and Q ​

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