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