Math, asked by Anonymous, 1 year ago

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✨ Please solve the following question✨

If the point C(-2,3) is equidistant from the points A(3,-1) and B(x,8), find the value of x. Also,find the distance BC.

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Answers

Answered by Mylo2145
9

Given that, C is equidistant from A and B.

i.e. AC = BC

By distance formula,

 \tt \sqrt{ {(3 + 2)}^{2} +  {( - 1 - 3)}^{2}  }  =  \sqrt{ {(x + 2)}^{2} +  {(8 - 3)}^{2}  }  \\  \\  \tt \sqrt{ {5}^{2} +  {( - 4)}^{2}  }  =  \sqrt{ {x}^{2} + 4 + 4x +  {(5)}^{2}  }  \\  \\  \tt \sqrt{25 + 16}  =  \sqrt{ {x}^{2}  + 4x + 4 + 25}  \\  \\  \tt  \huge{squaring \: both \: sides} \\  \\ \tt 41 =  {x}^{2}  + 4x + 29 \\  \\ \tt  {x}^{2}   + 4x - 12 = 0 \\  \\   \tt{x}^{2}  + 6x - 2x - 12 = 0 \\  \\  \tt x(x + 6) - 2(x  + 6) = 0 \\  \\  \tt(x - 2)(x + 6) = 0 \\  \\ x = 2 \: or \:  - 6


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Answered by Dhruv511vaja
0

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