Question

if the distance between (2,3) and (k,1) is 2 root 2. find the value of k

Answer 1

Refer to the attachement above

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Priyoshi...❤

Answer 2

$Distance \:between\: (x_1,y_1) \: and \: (x_2,y_2) \: are \: given \: as \\ d = \sqrt{ {( y_{2} - y_{1} )}^{2} + {( x_{2} - x_{1} )}^{2} } \\ 2 \sqrt{2} = \sqrt{ {(1 - 3 )}^{2} + {( k - 2 )}^{2} } \\ 2 \sqrt{2} = \sqrt{ {4 }+ {( k - 2 )}^{2} } \\ (2 \sqrt{2}) ^{2} = {4 }+ {( k - 2 )}^{2} \\ 8 = 4 + {(k - 2)}^{2} \\ {(k - 2)}^{2} = 4 \\ k - 2= 2 \\ k = 4$