# 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

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.

#### 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