1. **Match the quotes to the correct reflection rules:** - D. Reflection across the x-axis: $(x, y) \to (x, -y)$ matches quote D: "To reflect the figure, all x values will remain the same; all y values will take the opposite sign." - Reflection across the y-axis: $(x, y) \to (-x, y)$ matches quote A: "To reflect the figure, all x values will take the opposite sign; all y values will remain the same." - Reflection across line $y = x$: $(x, y) \to (y, x)$ matches quote C: "To reflect the figure, all x values will be the y values; all y values will be the x values." - Reflection across line $y = -x$: $(x, y) \to (-y, -x)$ matches quote B: "To reflect the figure, all x values will be the opposite sign of the y values; all y values will be the opposite sign of the x values." 2. **Reflection across the x-axis for points S(3,4), T(3,1), U(-2,1), V(-2,4):** - Transformation rule: $(x, y) \to (x, -y)$ - Calculate images: - $S(3,4) \to S'(3, -4)$ - $T(3,1) \to T'(3, -1)$ - $U(-2,1) \to U'(-2, -1)$ - $V(-2,4) \to V'(-2, -4)$ 3. **Reflection across the line $y = x$ for points D(-1,1), E(3,2), F(4,-1), G(-1,-3):** - Transformation rule: $(x, y) \to (y, x)$ - Calculate images: - $D(-1,1) \to D'(1, -1)$ - $E(3,2) \to E'(2, 3)$ - $F(4,-1) \to F'(-1, 4)$ - $G(-1,-3) \to G'(-3, -1)$ This completes the matching and the reflections with their transformation rules and image points.