1. **State the problem:** We start with point $P(-6,1)$ and apply a series of transformations in the order given. 2. **List the transformations:** - Reflection over the y-axis - Translation: $(x,y) \to (x-6,y)$ - 180° rotation clockwise about the origin - Reflection over the x-axis - Reflection over the y-axis - Translation: $(x,y) \to (x-1,y-1)$ - Dilation: $(x,y) \to (2.5x,2.5y)$ - Reflection over the y-axis 3. **Apply each transformation step-by-step:** **Step 1: Reflection over the y-axis** Reflection over the y-axis changes $(x,y)$ to $(-x,y)$. $$P_1 = (-(-6),1) = (6,1)$$ **Step 2: Translation $(x,y) \to (x-6,y)$** Subtract 6 from the x-coordinate: $$P_2 = (6-6,1) = (0,1)$$ **Step 3: 180° rotation clockwise about the origin** A 180° clockwise rotation about the origin sends $(x,y)$ to $( -x, -y )$. $$P_3 = (-0,-1) = (0,-1)$$ **Step 4: Reflection over the x-axis** Reflection over the x-axis sends $(x,y)$ to $(x,-y)$. $$P_4 = (0,-(-1)) = (0,1)$$ **Step 5: Reflection over the y-axis** Reflection over the y-axis sends $(x,y)$ to $(-x,y)$. $$P_5 = (-(0),1) = (0,1)$$ **Step 6: Translation $(x,y) \to (x-1,y-1)$** Subtract 1 from both coordinates: $$P_6 = (0-1,1-1) = (-1,0)$$ **Step 7: Dilation $(x,y) \to (2.5x,2.5y)$** Multiply both coordinates by 2.5: $$P_7 = (2.5 \times -1, 2.5 \times 0) = (-2.5,0)$$ **Step 8: Reflection over the y-axis** Reflection over the y-axis sends $(x,y)$ to $(-x,y)$. $$P_8 = (-(-2.5),0) = (2.5,0)$$ 4. **Final answer:** The final location of the point after all transformations is $$\boxed{(2.5,0)}$$