1. **State the problem:** We have points $X(-5,7)$, $Y(-4,-11)$, and $Z(9,-6)$. They are reflected over the x-axis to points $X'$, $Y'$, and $Z'$. We need to find the coordinates of $X'$, $Y'$, and $Z'$. 2. **Reflection rule over the x-axis:** The transformation rule is $$(x,y) \to (x,-y)$$ This means the x-coordinate stays the same, and the y-coordinate changes sign. 3. **Apply the rule to each point:** - For $X(-5,7)$: $$X' = (-5, -7)$$ - For $Y(-4,-11)$: $$Y' = (-4, -(-11)) = (-4, 11)$$ - For $Z(9,-6)$: $$Z' = (9, -(-6)) = (9, 6)$$ 4. **Final answer:** $$X' = (-5, -7), \quad Y' = (-4, 11), \quad Z' = (9, 6)$$