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If the point A(x, 2) is equidistant from the points B(8, -2) a

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If the point $A (x, 2)$ is equidistant from the points $B (8, - 2)$ and $C (2, - 2)$ , find the value of x. Also, find the length of AB.

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Oliver Discussed

If the point

A (x, 2)

is equidistant from the points

B (8, - 2)

and

C (2, - 2)

, find the value of x. Also, find the length of AB.

12 mins ago

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12 mins ago

Text solutionVerified

Given: Point

A (x, 2)

is equidistant from

B (8, - 2)

and

C (2, - 2)

Which implies:

A B = A C

Squaring both sides

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

Using distance formula:

Distance formula:

PQ = (x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2}

We have,

(8 - x)^{2} + (- 2 - 2)^{2} = (2 - x)^{2} + (- 2 - 2)^{2}

(8 - x)^{2} + (- 4)^{2} = (2 - x)^{2} + (- 4)^{2}

64 - 16 x + x^{2} = 4 - 4 x + x^{2}

64 - 4 = - 4 x + 16 x

12 x = 60 \Rightarrow x = \frac{60}{12} = 5

A B = (8 - 5)^{2} + (- 4)^{2}

= 3^{2} + (- 4)^{2} = 9 + 16

= 25 = 5

units

x = 5, A B = 5

units.

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Question Text	If the point $A (x, 2)$ is equidistant from the points $B (8, - 2)$ and $C (2, - 2)$ , find the value of x. Also, find the length of AB.
Answer Type	Text solution:1
Upvotes	150