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Find the coordinates of the point equidistant from three given

Question

Find the coordinates of the point equidistant from three given points $A (5, 3), B (5, - 5)$ and $C (1, - 5)$ .

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Find the coordinates of the point equidistant from three given points

A (5, 3), B (5, - 5)

and

C (1, - 5)

5 mins ago

Discuss this question LIVE

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Text solutionVerified

Let the coordintaes of the point be

O (x, y)

, then

O A = OB = OC

O A^{2} = O B^{2} = O C^{2}

O A^{2} = (5 - x)^{2} + (3 - y)^{2}

O B^{2} = (5 - x)^{2} + (- 5 - y)^{2}

O C^{2} = (1 - x)^{2} + (- 5 - y)^{2}

(5 - x)^{2} + (3 - y)^{2} = (5 - x)^{2} + (- 5 - y)^{2}

9 - 6 y + y^{2} = 25 + 10 y + y^{2}

9 - 25 = 10 y + 6 y

\Rightarrow 16 y = - 16

y = \frac{- 16}{16} = - 1

and

(5 - x)^{2} + (- 5 - y)^{2}

= (1 - x)^{2} + (- 5 - y)^{2}

25 - 10 x + x^{2} = 1 - 2 x + x^{2}

- 10 x + 2 x = 1 - 25

- 8 x = - 24

x = 3

So, coordinates of the point is

(3, 1)

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Question Text	Find the coordinates of the point equidistant from three given points $A (5, 3), B (5, - 5)$ and $C (1, - 5)$ .
Answer Type	Text solution:1
Upvotes	151