Question

If the point A(0, 2) is equidistant from the points B(3, p) and C(p, 5), find the value of p. Also, find the length of AB.

Answer 1

As per the question

AB = AC

`⇒ sqrt((0-3)^2 +(2-p)^2 ) = sqrt((0-p)^2 + (2-5)^2)`

`⇒ sqrt((-3)^2 +(2-p)^2) = sqrt((-p)^2 + (-3)^2)`

Squaring both sides, we get

`(-3)^2 +(2-p)^2 = (-p)^2 +(-3)^2`

`⇒ 9+4+p^2-4p=p^2+9`

`⇒ 4p =4`

⇒ p=1

Now,

`AB = sqrt((0-3)^2 +(2-p)^2)`

`= sqrt((-3)^2 +(2-1)^2))`                 (∵p=1)

`=sqrt(9+1)`

`= sqrt(10)`  units

Hence, p = 1  and AB =`sqrt(10)` units