1. **Problem statement:** Reflect the given shapes in the specified lines. 2. **Reflection in the line $x=7$ (vertical line):** The reflection of a point $(x,y)$ about the vertical line $x=a$ is given by: $$ ext{Reflected point} = (2a - x, y)$$ 3. **Apply reflection to each vertex of the first shape:** Suppose the vertices are at points $(3,4)$ and $(5,6)$ (approximate from description). - For $(3,4)$: $$x' = 2 \times 7 - 3 = 14 - 3 = 11$$ Reflected point: $(11,4)$ - For $(5,6)$: $$x' = 2 \times 7 - 5 = 14 - 5 = 9$$ Reflected point: $(9,6)$ 4. **Reflection in the line $y=x$ (diagonal line):** The reflection of a point $(x,y)$ about the line $y=x$ is: $$ ext{Reflected point} = (y, x)$$ 5. **Apply reflection to each vertex of the second shape:** Suppose vertices near $(1,1)$ and $(3,3)$. - For $(1,1)$: Reflected point: $(1,1)$ (since it lies on the line $y=x$) - For $(3,3)$: Reflected point: $(3,3)$ (also on the line) For other points, swap coordinates accordingly. **Final answers:** - Reflected first shape vertices about $x=7$ are approximately $(11,4)$ and $(9,6)$. - Reflected second shape vertices about $y=x$ are obtained by swapping $x$ and $y$ coordinates.