Reflection Line 1Ca8Fb

1. **State the problem:** We need to reflect a quadrilateral with vertices at $ (4, -2), (6, -5), (8, -6), (9, -5) $ over the horizontal line $ y = -1 $. 2. **Formula for reflection over a horizontal line:** If a point is $ (x, y) $ and the reflection line is $ y = k $, the reflected point $ (x', y') $ is given by: $$ y' = 2k - y $$ The $x$-coordinate remains the same. 3. **Apply the formula to each vertex:** - For $ (4, -2) $: $$ y' = 2(-1) - (-2) = -2 + 2 = 0 $$ Reflected point: $ (4, 0) $ - For $ (6, -5) $: $$ y' = 2(-1) - (-5) = -2 + 5 = 3 $$ Reflected point: $ (6, 3) $ - For $ (8, -6) $: $$ y' = 2(-1) - (-6) = -2 + 6 = 4 $$ Reflected point: $ (8, 4) $ - For $ (9, -5) $: $$ y' = 2(-1) - (-5) = -2 + 5 = 3 $$ Reflected point: $ (9, 3) $ 4. **Summary:** The reflected quadrilateral has vertices at $ (4, 0), (6, 3), (8, 4), (9, 3) $. These points are the reflection of the original figure over the line $ y = -1 $.