Question

A rectangle is drawn in a coordinate plane with vertices (-2,4),(4,4)(4,0) and (-2,0) which of the following represents the dimensions of the rectangles. A. 1 unit by 3 units B. 2 units by 3 units C. 4 units by 6 units D. 6 units by 8 units

Answer 1

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,

`\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}`

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,

`\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}`

So the rectangle has sides 6 and 4 units.

Therefore, option C is the correct choice.