#### Questions

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.

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

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#### Solution

The given points are A(0, 2), B(3, *p*) and C(*p*, 5).

It is given that A is equidistant from B and C.

∴ AB = AC

⇒ AB^{2} = AC^{2}

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

⇒ 9 + *p*^{2} + 4 − 4*p* = *p*^{2} + 9

⇒ 4 − 4*p* = 0

⇒ 4*p* = 4

⇒ *p* = 1

Thus, the value of *p* is 1.

Length of AB `=sqrt((3-0)^2+(1-2)^2)=sqrt(3^2+(-1)^2)=sqrt(9+1)=sqrt(10) units`

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#### Reference Material

Solution for question: 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. concept: Distance Formula. For the course CBSE