3. $D(-1,1), E(3,2), F(4,-1), G(-1,-3)$ Reflection across $y=x$ Transformation Rule: $(x, y) \rightarrow$ \begin{tabular}{|c|c|} \hline $\begin{array}{c}\text { Preimage Coordinates } \\ (x, y)\end{array}$ & Image \\ \hline & \\ \hline & \\ \hline & \\ \hline \end{tabular}

Step 1 ：Given the points $D(-1,1)$, $E(3,2)$, $F(4,-1)$, and $G(-1,-3)$, we are asked to reflect these points across the line $y=x$.

Step 2 ：The transformation rule for reflection across the line $y=x$ is $(x, y) \rightarrow (y, x)$. This means that we swap the x and y coordinates of each point.

Step 3 ：Applying this transformation rule to each point, we get the reflected points $D'(1, -1)$, $E'(2, 3)$, $F'(-1, 4)$, and $G'(-3, -1)$.

Step 4 ：\(\boxed{\text{The reflected points are } D'(1, -1), E'(2, 3), F'(-1, 4), \text{ and } G'(-3, -1)}\)