Enter coordinate rule details
Example data table
| Rule | Input point | Settings | Mapped point |
|---|---|---|---|
| Translation | (2, 3) | dx = 3, dy = -2 | (5, 1) |
| Reflection across y-axis | (4, -1) | None | (-4, -1) |
| Rotation about origin | (1, 2) | 90° | (-2, 1) |
| Dilation about point | (5, 2) | Center (1, 1), scale 2 | (9, 3) |
Formula used
Translation: (x', y') = (x + a, y + b)
Reflection across x-axis: (x', y') = (x, -y)
Reflection across y-axis: (x', y') = (-x, y)
Reflection through origin: (x', y') = (-x, -y)
Reflection across y = x: (x', y') = (y, x)
Reflection across y = -x: (x', y') = (-y, -x)
Rotation about origin: x' = x cos θ - y sin θ, y' = x sin θ + y cos θ
Rotation about point (h, k): shift to the center, rotate, then shift back
Dilation about origin: (x', y') = (sx, sy)
Dilation about point (h, k): (x', y') = (h + s(x - h), k + s(y - k))
Custom rule: choose your own x' and y' expressions using x and y.
These formulas let you map single points or whole shapes. The calculator applies one rule to every input point and then reports the transformed coordinates.
How to use this calculator
- Enter each coordinate on a separate line using a label or plain values.
- Select the coordinate rule you want to test.
- Fill in the needed settings such as shifts, angle, center, scale, or custom expressions.
- Press the calculate button to generate the mapped coordinates.
- Review the result panel above the form for the rule summary, centroid changes, bounds, and transformed table.
- Use the CSV or PDF buttons to save the output for revision, class notes, or assignments.
Frequently asked questions
1. What does a coordinate rule calculator do?
It applies a chosen transformation rule to one point or many points. You can study how reflections, translations, rotations, dilations, or custom rules change coordinates.
2. Can I enter several points together?
Yes. Add one point per line in the points box. The calculator processes every line and shows all transformed coordinates in one result table.
3. How are rotations handled?
Rotation formulas use degrees for the standard rotation controls. The page converts the angle internally and returns mapped coordinates after the turn.
4. What is the difference between origin and point dilation?
Origin dilation scales distances from the origin. Point dilation scales distances from a chosen center, which is useful when a shape expands around another location.
5. Can I build my own rule?
Yes. Use the custom rule option and enter formulas for x' and y'. This is useful for special mappings, classroom experiments, or checking derived rules.
6. Why are centroid and bounds shown?
They help you compare the original set of points with the transformed set. This makes shifts, size changes, and orientation changes easier to spot quickly.
7. When should I export CSV or PDF?
Use CSV for spreadsheet work or classroom data analysis. Use PDF when you want a neat summary report for homework, revision sheets, or printed notes.
8. Does this help with school geometry problems?
Yes. It is useful for coordinate geometry lessons, transformation practice, exam checking, and verifying plotted image points after applying a rule.