Question

If a point A(0,2) is equidistant from the point B(3,p) and C(p,5), then find the value of p.​

Answer 1

Answer:

Given, AB=AC

= whole root of (0-3)^2 + (2-p)^2 = whole root of (0-p)^2 + (2-5)^2

= 9 + (2-p)^2 = p^2 + 9

= 4 + p^2 - 4p = p^2

4p =4

p = 1.

Substitute of p-value in AB

Length of AB = whole root of (0-3)^2 + (2-1)^2

= whole root of 9 + 1

= root 10.

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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.