Respuesta :
The cordinates of the vertices if the rectangle are given as (-2,4),(4,4)(4,0) and (-2,0).
Note that the side joining (4,0) and (-2,0) lies on the x-axis from point x=-2 to x=4.
So the length of this side is given by,
[tex]\begin{gathered} d_1=\sqrt[]{(0-0)^2+(-2-4)^2} \\ d_1=\sqrt[]{(-6)^2} \\ d_1=\sqrt[]{36} \\ d_1=6 \end{gathered}[/tex]Now, for any adjacent side one point should be any of the two above.
Consider the adjacent side joining the coordinates(4,0) and (4,4). The length of the side is given by,
[tex]\begin{gathered} d_2=\sqrt[]{(4-0)^2+(4-4)^2} \\ d_2=\sqrt[]{(4)^{2+(0)^2}} \\ d_2=\sqrt[]{16} \\ d_2=4 \end{gathered}[/tex]So the rectangle has sides 6 and 4 units.
Therefore, option C is the correct choice.
