Q14 of 47 Page 1

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


Given, AB = AC


Squaring on both sides, we get


AB2 = AC2


We know that the distance between P(x1, y1 ) and Q(x2, y2 ) is .


⇒ (3 – 0)2 + (p – 2)2 = (p – 0)2 + (5 – 2)2


⇒ 9 + p2 + 4 – 4p = p2 + 9


⇒ 9 + p2 + 4 – 4p - p2 - 9 = 0


⇒ –4p + 4 = 0


⇒ -4p = -4


⇒ p = 1


Now, AB =


⇒ AB =


=


∴ AB = √10 units


Ans. The value of p is 1 and the length of AB is √10 units.


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