Math Problem Statement
Graph the image of the figure below on a reflection over the x-axis.
Solution
To solve this reflection problem, we need to reflect each point of the figure over the x-axis.
Step-by-Step Solution:
-
Identify the coordinates of points Z, W, X, and Y from the original image:
- is at
- is at
- is at
- is at
-
Apply the reflection rule over the x-axis:
- Reflecting a point over the x-axis changes the -coordinate’s sign, resulting in .
-
Determine the coordinates of the reflected points:
- The reflection of will be .
- The reflection of will be .
- The reflection of will be .
- The reflection of will be .
-
Plot these new points on the graph:
- Place , , , and at their respective reflected coordinates.
- Connect the points , , , and in the same order as the original shape.
This will create the reflection of the figure over the x-axis.
Would you like a visual representation or have any specific questions about this solution?
Further Related Questions:
- How do you find the reflection of a point over the y-axis?
- What is the rule for reflecting a point over the origin?
- How would you reflect a shape over a line like ?
- Can you apply the same method to find a reflection over other lines?
- How do reflections affect the orientation of shapes?
Tip: When reflecting over the x-axis, only the y-coordinates change, flipping to their opposite values.
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Math Problem Analysis
Mathematical Concepts
Reflection
Coordinate Geometry
Formulas
Reflection over x-axis: (x, y) -> (x, -y)
Theorems
Reflection Theorem
Suitable Grade Level
Grades 8-10