Respuesta :
If two quadrilateral are plotted in the upper left and upper right quadrants, respectively and points correspond to A(-2,6), B(-4,12), C(-8,14) and D(-6,6). On the upper right, P(2,6), Q(4,12), R(8,14), and S(6,6) then the statement which shows that ABCD and PQRS are congruent is option B which is corrsponding pairs of sides on ABCD and PQRS are equal in length.
Given coordinates of A(-2,6), B(-4,12), C(-8,14) , D(-6,6) and P(2,6), Q(4,12), R(8,14), and S(6,6).
PQ=[tex]\sqrt{(4-2)^{2} +(12-6)^{2} }[/tex]
=[tex]\sqrt{2^{2} +6^{2} }[/tex]
=[tex]\sqrt{4+36}[/tex]
=[tex]\sqrt{40}[/tex] units
AB=[tex]\sqrt{(-4-2)^{2} +(12-6)^{2} }[/tex]
=[tex]\sqrt{(-2)^{2} +(6)^{2} }[/tex]
=[tex]\sqrt{4+36}[/tex]
=[tex]\sqrt{40}[/tex] units
QR=[tex]\sqrt{(8-4)^{2} +(14-12)^{2} }[/tex]
=[tex]\sqrt{(4)^{2} +(2)^{2} }[/tex]
=[tex]\sqrt{16+4}[/tex]
=[tex]\sqrt{20}[/tex]units
BC=[tex]\sqrt{(-8+4)^{2} +(14-12)^{2} }[/tex]
=[tex]\sqrt{4+64 }[/tex]
=[tex]\sqrt{68}[/tex] units
RS=[tex]\sqrt{(6-8)^{2} +(6-14)^{2} }[/tex]
=[tex]\sqrt{4+64 }[/tex]
=[tex]\sqrt{68}[/tex] units
CD=[tex]\sqrt{(-6-8)^{2} +(6-14)^{2} }[/tex]
=[tex]\sqrt{4+64}[/tex]
=[tex]\sqrt{68}[/tex] units
SP=[tex]\sqrt{(6-2)^{2} +(6-6)^{2} }[/tex]
=[tex]\sqrt{16}[/tex]
=4 units
DA=[tex]\sqrt{(-6+2)^{2} +(6-6)^{2} }[/tex]
=[tex]\sqrt{16}[/tex]
=4 units
AB=PQ,QR=BC,SR=DC,PS=AD.
Hence the right statement is that corresponding pairs of side ABCD and PQRS are equal in length.
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