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# Solution - 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. - CBSE Class 10 - Mathematics

ConceptDistance Formula

#### 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.

#### 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

⇒ AB2 = AC2

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

⇒ 9 + p2 + 4 − 4p = p2 + 9

⇒ 4 − 4p = 0

⇒ 4p = 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

Is there an error in this question or solution?

#### APPEARS IN

R.D. Sharma 10 Mathematics
Chapter 14: Co-Ordinate Geometry
Q: 44
2013-2014 (March) Delhi Set 1
Question 18 | 3 marks

#### 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
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