Question

If the point A(x, 2) is equidistant from the points B(8, –2) and C(2, –2), find the value of x. Also, find the length of AB.

Answer 1

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.