Q. 24.6( 5 Votes )

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

Answer :

According to question-

AB = AC

taking square on both sides, we get-

AB^{2} = AC^{2}

⇒ (0-3)^{2} + (2-p)^{2} = (0-p)^{2} + (2-5)^{2}

[using distance formula, the distance between points (x_{1},y_{1}) and (x_{2},y_{2}) is equal to units.]

⇒ 9 + 4 + p^{2} - 4p = p^{2} + 9

⇒ 4p-4 = 0

⇒ 4p = 4

∴ p = 1

Thus, the value of p is 1.

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