Math Problem Statement
Reflect the figure over the line y = -1.
Solution
The task in the image is to reflect the given figure over the line .
Steps to reflect a shape over the line :
- Identify the coordinates of the vertices of the polygon in the image. Let's call these points .
- Reflect each point across the line . To reflect a point over this line, the new y-coordinate is determined by the formula: The x-coordinate remains unchanged.
- Plot the new points after reflection and connect them in the same order to form the reflected shape.
Example of the reflection formula:
- If a point is above the line, for example, , the reflected point would be: So the reflected point would be .
Would you like me to walk through the reflection of each point in the figure, or would you like further clarification?
Here are some related questions for better understanding:
- What are the coordinates of the vertices of the original figure?
- How do you calculate reflections over other lines, like ?
- What is the general reflection rule for any horizontal line ?
- How does the process differ for reflecting over a vertical line, like ?
- How would this reflection change if the line of reflection was diagonal, like ?
Tip: When reflecting points over a horizontal line, only the y-coordinates change, but the x-coordinates stay the same!
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Math Problem Analysis
Mathematical Concepts
Geometry
Reflections
Coordinate Plane
Formulas
y' = -2 - y (for reflecting over y = -1)
Theorems
Reflection Theorem over a Horizontal Line
Suitable Grade Level
Grades 8-10