3. As shown in Figure 1, the diagonal $BD$ of rectangle $ABCD$ passes through the origin $O$, and the sides of the rectangle are parallel to the coordinate axes. Point $C$ lies on the graph of the inverse proportion function $y=\frac{3k+1}{x}$. If $A(-2,-2)$, then $k=(\quad)$.
(A) 2
(B) 1
(C) 0
(D) -1
3. B.

Since the diagonal of a rectangle bisects the rectangle, therefore,
$S_{\text {partCHOG }}=S_{\text {partOFAE }}=|-2| \times|-2|=4$.
Thus $3 k+1=O G \cdot G C=4 \Rightarrow k=1$.