Answer:
Area is 16
Step-by-step explanation:
To obtain the area of the shown rectangle we need to obtain the dimensions of its sides.
Since all we have are coordinates, we need to apply the equation for distance between points.
That is
[tex]d=\sqrt{(x_{2}-x_{1})^2 +(y_{2}-y_{1})^2 }[/tex]
To obtain BF.
(x2,y2)=(0,3)
(x1,y1)=(-2,1)
BF=SQRT(4+4)=SQRT(8)=2 sqrt(2)
To obtain BC
(x2,y2)=(4,-1)
(x1,y1)=(0,3)
BC=SQRT(16+16)=SQRT(32)=4 SQRT(2)
The area of the rectangle B C E F is the product BC*BF= (2*sqrt(2) * 4*sqrt(2))=(8*sqrt(2)*sqrt(2))=8*2=16
