Find the coordinates of the point equidistant from three given points A(5,1), B(-3.-7) and
C(7,-1).
Answers
Explanation:
given,
the point is equidistant from A(5,1) B(-3,-7) C(7,-1)
let D(x,y) which is equidistant from three points
AD=BD=CD
_________ __________ _________
√(x-5)²+(y-1)²=√(x+3)²+(y+7)²=√(x-7)²+(y+1)²
squaring on all sides
=>(x-5)²+(y-1)²=(x+3)²+(y+7)²=(x-7)²+(y+1)²
=>x²+25-10x+y²+1-2y=x²+9+6x+y²+49+14y=x²+49-14x+y²+1+2y
=>25-10x-2y+1=9+6x+49+14y=49-14x+1+2y
Take first and second equation
=>25-10x-2y+1=9+6x+49+14y
=>25-10x-2y+1-9-6x-49-14y=0
=>-16x-16y-32=0
=>-16(x+y+2)=0
=>x+y+2=0.......................(1)
Take first equation and third equation
=>25-10x-2y+1=49-14x+1+2y
=>25-10x-2y+1-49+14x-1-2y=0
=>4x-4y-24=0
=>4(x-y-6)=0
=>x-y-6=0......................(2)
Add (1) and (2)
=>x+y+2+x-y-6=0
=>2x-4=0
=>x=4/2=2
Substitute x=2 in (1)
=>2+y+2=0
=>y=-4
(x,y)=(2,-4)
HOPE U CAN UNDERSTAND
your answer is in the attachment
