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If the Poin A(0,2) is Equidistant Form the Points B (3, P) And C (P ,5) Find the Value of P. Also, Find the Length of Ab. - Mathematics

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

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Solution

As per the question

AB = AC

`⇒ sqrt((0-3)^2 +(2-p)^2 ) = sqrt((0-p)^2 + (2-5)^2)`

`⇒ sqrt((-3)^2 +(2-p)^2) = sqrt((-p)^2 + (-3)^2)`

Squaring both sides, we get

`(-3)^2 +(2-p)^2 = (-p)^2 +(-3)^2`

`⇒ 9+4+p^2-4p=p^2+9`

`⇒ 4p =4`

⇒ p=1

Now,

`AB = sqrt((0-3)^2 +(2-p)^2)`

`= sqrt((-3)^2 +(2-1)^2))`                 (∵p=1)

`=sqrt(9+1)`

`= sqrt(10)`  units

Hence, p = 1  and AB =`sqrt(10)` units 

Concept: Coordinate Geometry
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APPEARS IN

RS Aggarwal Secondary School Class 10 Maths
Chapter 16 Coordinate Geomentry
Q 7

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