Answer
See below
Work Step by Step
Let $x=(1,1) \in R^2\\
y_1=(-\frac{1}{2},-\frac{1}{2})\\
y_2=(-\frac{3}{2},-\frac{1}{2})\\
y_3=(-\frac{3}{2},-\frac{3}{2})\\
y_4=(-\frac{1}{2},-\frac{3}{2}) \in R^2$
Obtain:
$x+y_1=(1,1)+(-\frac{1}{2},-\frac{1}{2})=(1-\frac{1}{2},1-\frac{1}{2})=(\frac{1}{2},\frac{1}{2})$ is a vector in the first quadrant of $R^2$
$x+y_2=(1,1)+(-\frac{3}{2},-\frac{1}{2})=(1-\frac{3}{2},1-\frac{1}{2})=(-\frac{1}{2},\frac{1}{2})$ is a vector in the second quadrant of $R^2$
$x+y_3=(1,1)+(-\frac{3}{2},-\frac{3}{2})=(1-\frac{3}{2},1-\frac{3}{2})=(-\frac{1}{2},-\frac{1}{2})$ is a vector in the third quadrant of $R^2$
$x+y_4=(1,1)+(-\frac{1}{2},-\frac{3}{2})=(1-\frac{1}{2},1-\frac{3}{2})=(\frac{1}{2},-\frac{1}{2})$ is a vector in the fourth quadrant of $R^2$
