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