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Question
If the point A(x,2) is equidistant form the points B(8,-2) and C(2,-2) , find the value of x. Also, find the value of x . Also, find the length of AB.
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Solution
As per the question
AB = AC
`⇒ sqrt((x-8)^2+(2+2)^2 ) = sqrt((x-2)^2 +(2+2)^2)`
Squaring both sides, we get
`(x-8)^2 +4^2 = (x - 2)^2 +4^2`
`⇒ x^2 -16x+64+16=x^2+4-4x+16`
`⇒ 16x-4x=64-4`
`⇒ x = 60/12=5`
Now,
`AB = sqrt((x-8)^2 +(2+2)^2)`
`= sqrt((5-8)^2 +(2+2)^2) (∵ x =2)`
`=sqrt((-3)^2 +(4)^2)`
`=sqrt(9+16) = sqrt(25)=5`
Hence, x = 5and AB = 5 units.
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