Question

Show that the points p(2, 1), q(-1, 3), r( -5, -3) and s(-2, -5) are the vertices of a square

Answer 1

Let P(2,1), Q(-1,3), R(-5,-3) and S(-2,-5) be the given points .

/* One way of showing that PQRS is a square is to use the property that all its sides should be equal and both it's diagonals should also be equal. Now

$\underline {\pink { By\:using \:distance \: formula: }}$

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

$So \: sides \:are \\PQ = \sqrt{ (-1 - 2)^{2} + ( 3 - 1 )^{2}} \\= \sqrt{ (-3)^{2} + 2^{2}} \\= \sqrt{9+4}\\= \sqrt{13} \: units\: ---(1)$

$So \: sides \:are \\QR = \sqrt{ (-5 + 1)^{2} + ( -3 - 3)^{2}} \\= \sqrt{ (-4)^{2} + (-6)^{2}} \\= \sqrt{16+36}\\= \sqrt{52} \: units \: ---(2)$

$PQ ≠ QR \: [ From \: (1) \:and \: (2) ]$

Therefore.,

$\blue { PQRS \: points \: not \: form \: a \: square . }$

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Answer 2

quadrilateral PQRS point not form a square