Respuesta :
Given data:
The given vertices of the parallelogram are K(2, 7), L(6, 12), M(13, 13) and N(9, 8).
In parallelogram opposite sides are equal and parallel.
[tex]\begin{gathered} KL=\sqrt[]{(6-2)^2+(12-7)^2} \\ =\sqrt[]{4^2+5^2} \\ =\sqrt[]{16+25} \\ =\sqrt[]{41} \end{gathered}[/tex]The slope of KL is,
[tex]\begin{gathered} m=\frac{12-7}{6-2} \\ =\frac{5}{4} \end{gathered}[/tex]The measuremment of the side MN is,
[tex]\begin{gathered} MN=\sqrt[]{(9-13)^2+(8-13)^2} \\ =\sqrt[]{16+25} \\ =\sqrt[]{41} \end{gathered}[/tex]The slope of the MN is,
[tex]\begin{gathered} m^{\prime}=\frac{8-13}{9-13} \\ =\frac{-5}{-4} \\ =\frac{5}{4} \end{gathered}[/tex]The LM length is,
[tex]\begin{gathered} LM=\sqrt[]{(13-6)^2+(13-12)^2} \\ =\sqrt[]{49+1} \\ =\sqrt[]{50} \end{gathered}[/tex]The slope of LM is,
[tex]\begin{gathered} m_1=\frac{13-12}{13-6} \\ =\frac{1}{7} \end{gathered}[/tex]The length NK is,
[tex]\begin{gathered} NK=\sqrt[]{(2-9)^2+(7-8)^2} \\ =\sqrt[]{49+1} \\ =\sqrt[]{50} \end{gathered}[/tex]The slope of NK is,
[tex]\begin{gathered} m_2=\frac{7-8}{2-9} \\ =\frac{-1}{-7} \\ =\frac{1}{7} \end{gathered}[/tex]As, the opposite sides are equal and parallel, so the given quadrilaterl KLMN is parallelogram.
Thus, Yes it is parallelogram, so first option is correct.
