Question

Select the correct answer.

Answer 1

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=$\sqrt{(4-2)^{2} +(12-6)^{2} }$

=$\sqrt{2^{2} +6^{2} }$

=$\sqrt{4+36}$

=$\sqrt{40}$ units

AB=$\sqrt{(-4-2)^{2} +(12-6)^{2} }$

=$\sqrt{(-2)^{2} +(6)^{2} }$

=$\sqrt{4+36}$

=$\sqrt{40}$ units

QR=$\sqrt{(8-4)^{2} +(14-12)^{2} }$

=$\sqrt{(4)^{2} +(2)^{2} }$

=$\sqrt{16+4}$

=$\sqrt{20}$units

BC=$\sqrt{(-8+4)^{2} +(14-12)^{2} }$

=$\sqrt{4+64 }$

=$\sqrt{68}$ units

RS=$\sqrt{(6-8)^{2} +(6-14)^{2} }$

=$\sqrt{4+64 }$

=$\sqrt{68}$ units

CD=$\sqrt{(-6-8)^{2} +(6-14)^{2} }$

=$\sqrt{4+64}$

=$\sqrt{68}$ units

SP=$\sqrt{(6-2)^{2} +(6-6)^{2} }$

=$\sqrt{16}$

=4 units

DA=$\sqrt{(-6+2)^{2} +(6-6)^{2} }$

=$\sqrt{16}$

=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.

Learn more about congruency at brainly.com/question/2938476

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