Question

if(-2. 4) and (6.8) are the opposite
ends of a square, then the length of the side of the square is​

Answer 1

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Answer 2

HEY MATE HERE IS YOUR ANSWER :-

A and C are the point of ABCD square so AC is diagonal

A=(-2,4)

C=(6,8)

$ac = \sqrt{ {(6 + 2)}^{2} + {(8 - 4)}^{2} } \\ \: \: \: \: \: \: = \sqrt{ {8}^{2} + {4}^{2} } \\ \: \: \: \: \: \: = \sqrt{64 + 16} \\ \: \: \: \: \: \: = \sqrt{80}$

$ac = 4 \sqrt{5} \: units$

as AC is diagonal

${ac}^{2} = {x}^{2} + {x}^{2} \\ {(4 \sqrt{5}) }^{2} = 2 {x}^{2} \\ 80 = 2 {x}^{2} \\ {x}^{2} = 40 \\ x = \sqrt{40}$

$x = 2 \sqrt{10} \: units$

length of side is 2√10 units

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