Question

find the coordinates of the point equidistant from three given point A(5,3) ,B (5,-5) C(1,-5)​

Answer 1

Answer:

Let the coordintaes of the point be O(x,y), then

OA=OB=OC

or OA

2

=OB

2

=OC

2

OA

2

=(5−x)

2

+(3−y)

2

OB

2

=(5−x)

2

+(−5−y)

2

OC

2

=(1−x)

2

+(−5−y)

2

(5−x)

2

+(3−y)

2

=(5−x)

2

+(−5−y)

2

9−6y+y

2

=25+10y+y

2

9−25=10y+6y

⇒16y=−16

y=

16

−16

=−1

and (5−x)

2

+(−5−y)

2

=(1−x)

2

+(−5−y)

2

25−10x+x

2

=1−2x+x

2

−10x+2x=1−25

−8x=−24

or x=3

So, coordinates of the point is (3,1).

hope it's helpful for you ✌️✌️