2. (10 points) Choose the correct statements, assuming that $A$ is the area of a square with a diagonal of $2 \sqrt{2}$, $B$ is the area of a rectangle whose center and two adjacent vertices have coordinates $(2,2)$, $(4,1)$, and $(4,3)$ respectively, and $C$ is the area of the triangle formed by the coordinate axes and the line $y=-x / 2+2$.
a) $A<B$ or $B<C$.

b) $A=C \cup B<C$.

c) $C<A<B$.
d) $A=C$ or $C<B$.
Answer: a) and d).

Solution: It is not difficult to see that

- $A=4 \cdot \frac{1}{2} \cdot \sqrt{2} \cdot \sqrt{2}=4$
- the coordinates of the two remaining vertices of the rectangle will be $(0,3)$ and $(0,1)$ - these are the coordinates of the points symmetric to the points $(4,1)$ and $(4,3)$ with respect to the point $(2,2)$, so $B=8$;
- the line $y=-x / 2+2$ intersects the y-axis at the point $(0,2)$, and the x-axis at the point $(4,0)$, hence $C=\frac{1}{2} \cdot 2 \cdot 4=4$.

From this, we get that in statement a) the first inequality is true, so the entire statement is true; in statement b) the first condition is true, but the second is false, so the entire statement is false; statement c) is obviously false; in statement d) both the equality and the inequality are true, so the entire statement is also true.