Let a be a positive integer. In the rectangular coordinate plane, the triangular region between the line $x + y = 2$ and the axes is divided into two regions by the curve $y = x ^ { a }$ as shown in the figure.
In the figure; the area of region $A _ { 2 }$ is 2 times the area of region $A _ { 1 }$.\\
Accordingly, what is the value of a?\\
A) 2\\
B) 3\\
C) 4\\
D) 5\\
E) 6