Math, asked by shailesh6566, 5 hours ago

The distance between the points (−1,4) and (3,k) is square root 20 By forming an equation in , find the possible values of k.

Answers

Answered by xSoyaibImtiazAhmedx
1

Given ,

  • The distance between the points A(−1,4) and B(3,k) is square root 20.

To find :-

  • The value of k .

A/Q,

 \sqrt{(3 - ( - 1))^{2} +  {(k - 4)}^{2}  }  =  \sqrt{20}

 \implies \sqrt{(3  +  1)^{2} +  {(k - 4)}^{2}  }  =  \sqrt{20}

\implies {(4)^{2} +  {(k - 4)}^{2}  }  = 20

\implies 16 +   {k}^{2} - 8k + 16 = 20

\implies   {k}^{2} - 8k +32 - 20 = 0

\implies   {k}^{2} - 8k +12 = 0

\implies   {k}^{2} - 6k - 2k +12 = 0

\implies   k(k - 6)- 2(k - 6) = 0

\implies   (k - 6)(k - 2) = 0

\implies   k - 6 = 0 \:  \:  \:  \:  \:  \:  \:  \: or \:  \:  \:  \:  \:  \:  \:  k - 2 = 0

\implies    \boxed {\bold{k  = 6\:  \:  \:  \:  \:  \:  \:  \: or \:  \:  \:  \:  \:  \:  \:  k  = 2}}

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