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If a point A(0,2) is equidistant from the points B(3,p) and C(

Question

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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If a point

A (0, 2)

is equidistant from the points

B (3, p)

and

C (p, 5)

then find the value of

p .

12 mins ago

Discuss this question LIVE

12 mins ago

Text solutionVerified

Distance between two points=

(x_{2} - x_{1})^{2} (y_{2} - y_{1})^{2}

∴ A B = (0 - 3)^{2} + (2 - p)^{2}

\Rightarrow 9 + 4 - 4 p + p^{2}

\Rightarrow p^{2} - 4 p + 13

∴ A C = (p - 0)^{2} + (5 - 2)^{2}

\Rightarrow p^{2} + 9

As given

A B = A C

\Rightarrow p^{2} - 4 p + 13 = p^{2} + 9

Squaring both sides

\Rightarrow p^{2} - 4 p + 13 = p^{2} + 9

\Rightarrow - 4 p = 9 - 13

\Rightarrow - 4 p = - 4

\Rightarrow p = \frac{- 4}{- 4} = 1

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Question Text	If a point $A (0, 2)$ is equidistant from the points $B (3, p)$ and $C (p, 5)$ then find the value of $p .$
Answer Type	Text solution:1
Upvotes	151