📚 Topic Summary
Reflecting a point over the line $y = x$ involves swapping the x and y coordinates. So, if you have a point $(a, b)$, its reflection over $y = x$ is $(b, a)$. Reflecting a point over the line $y = -x$ involves swapping the x and y coordinates and then negating both. So, if you have a point $(a, b)$, its reflection over $y = -x$ is $(-b, -a)$. These transformations create a mirror image of the original point or shape across the specified line.
🧠 Part A: Vocabulary
Match each term with its definition:
- Reflection over y=x
- Reflection over y=-x
- Coordinate Plane
- Transformation
- Image
Definitions:
- A change in the position, size, or shape of a figure.
- The coordinate grid formed by the intersection of a horizontal number line (x-axis) and a vertical number line (y-axis).
- $(a, b)$ becomes $(-b, -a)$.
- $(a, b)$ becomes $(b, a)$.
- The resulting figure after a transformation.
Match each term (1-5) with the correct definition (a-e).
✏️ Part B: Fill in the Blanks
Complete the sentences with the correct words:
When reflecting over the line y=x, the x and y __________ are __________. For example, the point (2, 5) becomes (____, ____). When reflecting over the line y=-x, the x and y coordinates are also __________ but also __________. The point (3, -1) becomes (____, ____).
🤔 Part C: Critical Thinking
Explain, in your own words, how reflections over y=x and y=-x are similar and how they are different.
