see the attached figure with letters to better understand the problem
we know that
If the figure is a rectangle
then
[tex]AB=CD \\AD=BC[/tex]
The area of the rectangle is equal to
[tex]A=B*h[/tex]
where
B is the base
h is the height
the base B is equal to the distance AB
the height h is equal to the distance AD
Step 1
Find the distance AB
the formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
[tex]A(-5,5)\\B(0,-5)[/tex]
substitute the values
[tex]d=\sqrt{(-5-5)^{2}+(0+5)^{2}}[/tex]
[tex]d=\sqrt{(-10)^{2}+(5)^{2}}[/tex]
[tex]dAB=\sqrt{125}\ units[/tex]
Step 2
Find the distance AD
the formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
[tex]A(-5,5)\\D(-1,7)[/tex]
substitute the values
[tex]d=\sqrt{(7-5)^{2}+(-1+5)^{2}}[/tex]
[tex]d=\sqrt{(2)^{2}+(4)^{2}}[/tex]
[tex]dAD=\sqrt{20}\ units[/tex]
Step 3
Find the area of the rectangle
[tex]A=AB*AD[/tex]
we have
[tex]dAB=\sqrt{125}\ units[/tex]
[tex]dAD=\sqrt{20}\ units[/tex]
substitute
[tex]A=\sqrt{125}*\sqrt{20}[/tex]
[tex]A=\sqrt{2,500}[/tex]
[tex]A=50\ units^{2}[/tex]
therefore
the answer is the option
[tex]50\ units^{2}[/tex]
