📚 Topic Summary
Reflecting a point across the line $y = x$ involves swapping the $x$ and $y$ coordinates. So, a point $(a, b)$ becomes $(b, a)$. Reflecting across the line $y = -x$ involves swapping the $x$ and $y$ coordinates and then negating both. Thus, a point $(a, b)$ becomes $(-b, -a)$. These transformations create mirror images of geometric figures with respect to the lines $y=x$ and $y=-x$.
🧠 Part A: Vocabulary
| Term |
Definition |
| 1. Reflection across $y=x$ |
A. A transformation where the x and y coordinates are swapped and negated. |
| 2. Reflection across $y=-x$ |
B. A transformation that flips a figure over the line $y=x$. |
| 3. Image |
C. The new figure that results from a transformation. |
| 4. Pre-image |
D. The original figure before a transformation. |
| 5. Transformation |
E. A change in the position, size, or shape of a figure. |
Match the term to its correct definition:
- 🔍 1 - B
- 💡 2 - A
- 📝 3 - C
- 📊 4 - D
- 🌍 5 - E
✍️ Part B: Fill in the Blanks
When reflecting a point across the line $y = x$, the $x$ and $y$ coordinates are _____. For example, the point $(2, 5)$ becomes _____. On the other hand, when reflecting across the line $y = -x$, the $x$ and $y$ coordinates are _____ and then _____. For example, the point $(3, -1)$ becomes _____.
- 🧪 swapped
- 🧬 $(5, 2)$
- 🔬 swapped
- 📚 negated
- 📐 $(1, -3)$
🤔 Part C: Critical Thinking
Explain how reflecting a shape across $y = x$ and then across $y = -x$ is related to a rotation. What is the angle of rotation and the center of rotation?