Reflection Across the Line y = x
Grade 7 students in Big Ideas Math Advanced 2 (Chapter 2: Transformations) learn that reflecting a point across the line y = x swaps the x and y coordinates: (a, b) becomes (b, a). Points on the line y = x remain fixed since swapping equal values gives the same point.
Key Concepts
When a point $(a, b)$ is reflected across the line $y = x$, the resulting point is $(b, a)$. The $x$ coordinate and $y$ coordinate are swapped. The line $y = x$ acts as a mirror, where each point and its reflection are equidistant from this line.
Common Questions
What is the rule for reflecting across y = x in 7th grade?
When reflecting a point (a, b) across the line y = x, the result is (b, a). Simply swap the x and y coordinates.
How do you reflect the point (3, 7) across y = x?
Swap the coordinates: (3, 7) becomes (7, 3).
What happens to points on the line y = x when reflected?
Points on y = x have equal coordinates (e.g., (4, 4)). Swapping gives the same point, so they remain fixed.
What chapter in Big Ideas Math Advanced 2 covers reflection across y = x?
Chapter 2: Transformations in Big Ideas Math Advanced 2 (Grade 7) covers reflection across the line y = x.
Why does reflecting across y = x swap coordinates?
The line y = x is the diagonal mirror. Reflecting over it flips the roles of horizontal (x) and vertical (y) distances, which is equivalent to swapping the two coordinates.