Find the Area of the Region Whose Image Under the Transformation

Multiple Choice

Find the area of the region whose image under the transformation x = u + v, y = v - 2u is $D = \left\{ ( x , y ) \mid - 1 \leq x \leq 1,0 \leq y \leq 1 - x ^ { 2 } \right\}$ .

A) $\frac { 1 } { 9 }$

B) $\frac { 2 } { 9 }$
C) $\frac { 1 } { 3 }$
D) $\frac { 4 } { 9 }$
E) $\frac { 5 } { 9 }$
F) $\frac { 2 } { 3 }$

G) $\frac { 7 } { 9 }$

H) $\frac { 8 } { 9 }$