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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. - Mathematics

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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.

Concept: Distance Formula
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APPEARS IN

RS Aggarwal Secondary School Class 10 Maths
Chapter 16 Coordinate Geomentry
Q 6

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