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Reflecting Across y=x
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Reflecting Across y=x
📚 Part 1: Understanding the Line y = x
1. The line y = x passes through which of these points?
(2, 3)
(4, 4)
(1, 5)
(3, 2)
2. When reflecting across y = x, what happens to the coordinates (x, y)?
They stay the same: (x, y)
They swap positions: (y, x)
They become negative: (-x, -y)
Only the x-coordinate changes
3. Point A is at (3, 1). After reflecting across y = x, where is point A'?
(3, 1)
(1, 3)
(-3, -1)
(3, -1)
✏️ Part 2: Coordinate Practice
4. Complete the table by finding the reflected coordinates:
| Original Point | Reflected Point across y = x |
|---|---|
| (2, 5) | ( ____ , ____ ) |
| (0, 4) | ( ____ , ____ ) |
| (6, 2) | ( ____ , ____ ) |
| (1, 7) | ( ____ , ____ ) |
5. Triangle ABC has vertices at A(1, 3), B(2, 1), and C(4, 2). Find the coordinates of triangle A'B'C' after reflecting across y = x:
A' = ( ____ , ____ )
B' = ( ____ , ____ )
C' = ( ____ , ____ )
🎨 Part 3: Drawing and Analysis
6. Use the grid below to draw the line y = x, then reflect the given triangle across this line:
Grid space for drawing (plot original triangle at vertices (1,2), (3,1), (2,4) and reflect across y = x)
7. After reflecting a shape across y = x, which properties stay the same? (Tick all that apply)
Size of the shape
Shape (congruent)
Position
Angles within the shape
8. Explain in your own words how to reflect a point across the line y = x:
9. Extension: If point P is at (a, b), what would be the coordinates after reflecting across y = x, then across the y-axis?
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