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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?

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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: null - Distance Formula. For the course CBSE
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