Question: Reflections
Name: Cora Shivelman
S1 S2 S3 S4
MEDIUM
Graph the image of the figure using the given transformations.
1) reflection across the y-axis
2) reflection across the x-axis
3) reflection across the x-axis
4) reflection across the y-axis
5) reflection across the y-axis
6) reflection across the y-axis
top-left: Reflection worksheet title and name/class area.
top-right: Header with “MEDIUM”.
center: Six coordinate-grid graphs showing reflected polygon shapes in each problem box.
bottom-left: Problem 5 graph.
bottom-right: Problem 6 graph.
1. **Problem Statement:**
We are asked to graph the image of a figure after applying reflections across the x-axis or y-axis as specified in six different problems.
2. **Reflection Rules:**
- Reflection across the y-axis: The point $(x,y)$ maps to $(-x,y)$.
- Reflection across the x-axis: The point $(x,y)$ maps to $(x,-y)$.
3. **Step-by-step for each reflection:**
For each vertex of the polygon, apply the corresponding reflection rule.
**Example:**
- If a vertex is at $(3,2)$ and the reflection is across the y-axis, the image vertex is $(-3,2)$.
- If a vertex is at $(3,2)$ and the reflection is across the x-axis, the image vertex is $(3,-2)$.
4. **Apply to all vertices:**
For each problem (1 to 6), apply the reflection to all vertices of the polygon to get the reflected image.
5. **Graphing:**
Plot the original polygon and the reflected polygon on the coordinate grid for each problem.
6. **Summary:**
- Reflection across y-axis flips the figure horizontally.
- Reflection across x-axis flips the figure vertically.
Since the problem involves graphing and multiple images, the key is to apply the reflection formulas to each vertex and plot accordingly.