Question

If a point a(0,2) is equidistant from the points b(3,p) and c(p,5) then find value of p and the length of ab ?

Answer 1

Given, ab=ac
squaring on both sides
               (ab)^2=(ac)^2
(0-3)^2+(2-p)^2=(p-0)^2+(5-2)^2
     9+4+p^2-4p= p^2+9
                    4p=4
                      p=1
length of ab is (10)^1/2

Answer 2

Answer:

AB = AC

⇒AB =√(3-0)²+(p-2)² and AC =√(p-0)² + (5-2)²

⇒(3-0)² + (p-2)² =(p-0)² + (5-2)²

⇒9 + p² + 4 - 4p = p² + 9

⇒9 - 9 +p² - p² +4 -4p =0

⇒4 - 4p=0

⇒-4p =-4

⇒p = 1

so p=1 is the answer.