Calculator
Choose a mode, enter values, and reflect them across y = x.
Example Data Table
| Example Type | Original Input | Reflected Output | Rule Used |
|---|---|---|---|
| Point | (3, -1) | (-1, 3) | (x, y) → (y, x) |
| Line | y = 2x + 1 | y = 0.5x - 0.5 | Swap x and y, then solve. |
| Point Set | (1, 2), (3, -1), (-2, 4) | (2, 1), (-1, 3), (4, -2) | Reflect each point separately. |
Formula Used
How to Use This Calculator
- Select whether you want a point, line, or point-set reflection.
- Enter the required numeric values in the calculator fields.
- For point sets, place one coordinate pair on each line.
- Choose the number of decimal places for displayed values.
- Press the transform button to generate results and the graph.
- Review the summary cards, table, and plotted geometry.
- Use the CSV or PDF button to export your results.
FAQs
1. What does reflecting across y = x do?
It swaps every point’s x-coordinate and y-coordinate. A point at (a, b) becomes (b, a). The transformation mirrors shapes across the diagonal line y = x.
2. Why do the coordinates switch places?
The mirror line y = x contains points with equal coordinates. Reflection across that line exchanges horizontal and vertical distance, so x and y trade positions.
3. Can this calculator reflect full point sets?
Yes. Enter one coordinate pair per line in the point-set mode. The calculator reflects each point, builds a mapping table, and plots both sets.
4. How are lines reflected across y = x?
Replace y with x and x with y. For y = mx + b, the reflected relation becomes x = my + b. Then solve for y when possible.
5. What happens to a horizontal line?
A horizontal line y = b reflects to the vertical line x = b. That is why the transformed slope is undefined in that special case.
6. Is the transformation reversible?
Yes. Reflection across y = x is self-inverse. Apply the same reflection again, and every point or line returns to its original position.
7. Why is the distance formula included?
It measures how far the original point sits from the mirror line. Smaller values mean the point is closer to y = x before reflection.
8. When is this calculator useful?
It helps with coordinate geometry, graph sketching, matrix transformations, classroom demonstrations, and checking algebraic work involving reflections across diagonal axes.