Question

If the opposite vertices of a rectangle are (4,5) and (7,8) then the length of the diagonal is

Answer 1

$Given \: (4,5) \:and \: (7,8) \: are \: the$

$opposite \:vertices \: of \: a \: rectangle$

$\red{ Length \: of \: the \: diagonal }$

$= Distance \: of \: opposite \: vertices$

$= \sqrt{ (x_{2}-x_{1})^{2} + (y_{2}-y_{1})^{2}}$

$Here, x_{1} = 4 , \:y_{1} = 5$

$and \: x_{2} = 7 , \: y_{2} = 8$

$= \sqrt{ (7-4)^{2} + (8-5)^{2}}$

$= \sqrt{ 3^{2} + 3^{2}}$

$= \sqrt{ 9 + 9 }$

$= \sqrt{18}$

$= 3\sqrt{2}$

Therefore.,

$\red{ Length \: of \: the \: diagonal } \green { = 3\sqrt{2}}$

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