Figure Reflections Ba974B

1. **Problem Statement:** Reflect each given figure across the specified reflection line. 2. **Reflection Rules:** - Reflection across the $x$-axis: $(x,y) \to (x,-y)$. - Reflection across the vertical line $x = a$: $(x,y) \to (2a - x, y)$. - Reflection across the horizontal line $y = b$: $(x,y) \to (x, 2b - y)$. - Reflection across the line $y = x$: $(x,y) \to (y,x)$. --- ### a. Reflect across the $x$-axis - Each point $(x,y)$ of the figure becomes $(x,-y)$. - This flips the figure vertically, moving it from the bottom-right quadrant to the top-right quadrant. ### b. Reflect across the line $x = -3$ - Each point $(x,y)$ becomes $(2(-3) - x, y) = (-6 - x, y)$. - This moves the figure symmetrically to the left side of the line $x = -3$. ### c. Reflect across the line $y = 1$ - Each point $(x,y)$ becomes $(x, 2(1) - y) = (x, 2 - y)$. - This flips the figure vertically about the line $y=1$, moving it below that line. ### d. Reflect across the line $y = x$ - Each point $(x,y)$ becomes $(y,x)$. - This swaps the $x$ and $y$ coordinates, reflecting the figure across the diagonal line. --- **Summary:** - Use the formulas above to find the reflected coordinates of each vertex. - Plotting these new points will give the reflected figure. This completes the reflection transformations for all four parts.