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


According to question-


AB = AC


taking square on both sides, we get-


AB2 = AC2


⇒ (0-3)2 + (2-p)2 = (0-p)2 + (2-5)2


[using distance formula, the distance between points (x1,y1) and (x2,y2) is equal to units.]


⇒ 9 + 4 + p2 - 4p = p2 + 9


⇒ 4p-4 = 0


⇒ 4p = 4


∴ p = 1


Thus, the value of p is 1.


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