# 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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