Before we begin, note that we need to use the distanse formula for everything to reach our conclusion. With that being said, here we go:
![\displaystyle \sqrt{[-x_1 + x_2]^2 + [-y_1 + y_2]^2} = d](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Csqrt%7B%5B-x_1%20%2B%20x_2%5D%5E2%20%2B%20%5B-y_1%20%2B%20y_2%5D%5E2%7D%20%3D%20d)
Using the ordered pairs
and
for instanse:
![\displaystyle \sqrt{[-3 + 4]^2 + [3 - 2]^2} = \sqrt{1^2 + 1^2} = \sqrt{2}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Csqrt%7B%5B-3%20%2B%204%5D%5E2%20%2B%20%5B3%20-%202%5D%5E2%7D%20%3D%20%5Csqrt%7B1%5E2%20%2B%201%5E2%7D%20%3D%20%5Csqrt%7B2%7D)
Now, sinse the <em>distanse</em><em> </em>between
and
is
units, then the distanse between
and
ALSO has to be
units. By definition, lettre <em>c</em><em> </em>has already been answered for you because sinse it is a rectangle, if the two short sides are congruent, then the two long sides ALSO have to be congruent, but just in case you want to be sure [you do not trust your instincts], just simply re-use the distanse formula.
Using the ordered pairs
and
for instanse:
![\displaystyle \sqrt{[-1 + 4]^2 + [-1 - 2]^2} = \sqrt{3^2 + [-3]^2} = \sqrt{9 + 9} = \sqrt{18} = 3\sqrt{2}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Csqrt%7B%5B-1%20%2B%204%5D%5E2%20%2B%20%5B-1%20-%202%5D%5E2%7D%20%3D%20%5Csqrt%7B3%5E2%20%2B%20%5B-3%5D%5E2%7D%20%3D%20%5Csqrt%7B9%20%2B%209%7D%20%3D%20%5Csqrt%7B18%7D%20%3D%203%5Csqrt%7B2%7D)
So there you have it. The length of both of the long sides is
units.
Now that we cleared all of that up, we can now find the perimetre and area of this rectangle:

![\displaystyle 2[\sqrt{2}] + 2[3\sqrt{2}] = 2\sqrt{2} + 6\sqrt{2} = 8\sqrt{2}](https://tex.z-dn.net/?f=%5Cdisplaystyle%202%5B%5Csqrt%7B2%7D%5D%20%2B%202%5B3%5Csqrt%7B2%7D%5D%20%3D%202%5Csqrt%7B2%7D%20%2B%206%5Csqrt%7B2%7D%20%3D%208%5Csqrt%7B2%7D)
The perimetre of this rectangle is
<em>units</em>.

![\displaystyle [\sqrt{2}][3\sqrt{2}] = [3][2] = 6](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5B%5Csqrt%7B2%7D%5D%5B3%5Csqrt%7B2%7D%5D%20%3D%20%5B3%5D%5B2%5D%20%3D%206)
The area of this rectangle is
<em>squared units</em>.
You have now found what you were looking for.
** All rectangles are parallelograms because they both have two pairs of parallel and congruent sides, while vice versa is falce because a parallelogram does not have <em>four congruent right angles</em>, so it is safe to say that this is both a rectangle AND parallelogram, sinse the picture displayed is a rectangle.
I am joyous to assist you at any time. ☺️