Subjects geometry

Reflect Over Y= 1 9E6Bef

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1. **State the problem:** We need to reflect given points over the line $y = -1$. 2. **Formula and rule:** To reflect a point $(x,y)$ over the horizontal line $y = k$, the reflected point $(x',y')$ is given by: $$y' = 2k - y$$ The $x$-coordinate remains the same because the reflection is vertical. 3. **Explanation:** The line $y = -1$ is horizontal, so the vertical distance from the point to the line is $y - (-1) = y + 1$. The reflected point is the same distance on the opposite side, so: $$y' = -1 - (y + 1) = -1 - y - 1 = -2 - y$$ But using the formula $y' = 2k - y$ with $k = -1$ is simpler. 4. **Example:** If a point is $(x, y)$, its reflection over $y = -1$ is: $$x' = x$$ $$y' = 2(-1) - y = -2 - y$$ 5. **Summary:** To reflect any point over $y = -1$, keep $x$ the same and replace $y$ with $-2 - y$. This completes the reflection rule over $y = -1$.