Calculator Input
Enter one point per line as x,y or (x,y).
Example Data Table
| Transformation | Rule | Sample Input | Sample Output |
|---|---|---|---|
| Translation | (x, y) → (x + 2, y + 3) | (1, 2) | (3, 5) |
| Reflection in x-axis | (x, y) → (x, -y) | (4, -6) | (4, 6) |
| Reflection in y = x | (x, y) → (y, x) | (2, 7) | (7, 2) |
| Rotation about origin | 90° counterclockwise | (3, 1) | (-1, 3) |
| Dilation about origin | (x, y) → (2x, 2y) | (-2, 5) | (-4, 10) |
Formula Used
Coordinate transformations move or resize points by a fixed rule.
1. Translation
(x, y) → (x + a, y + b)
Here, a is the horizontal shift and b is the vertical shift.
2. Reflections
x-axis: (x, y) → (x, -y)
y-axis: (x, y) → (-x, y)
Origin: (x, y) → (-x, -y)
Line y = x: (x, y) → (y, x)
Line y = -x: (x, y) → (-y, -x)
Line x = k: (x, y) → (2k - x, y)
Line y = k: (x, y) → (x, 2k - y)
3. Rotation About the Origin
x′ = x cos θ - y sin θ
y′ = x sin θ + y cos θ
Positive angles rotate counterclockwise.
4. Rotation About a Custom Center (h, k)
x′ = h + (x-h)cos θ - (y-k)sin θ
y′ = k + (x-h)sin θ + (y-k)cos θ
5. Dilation
About origin: (x, y) → (sx, sy)
About center (h, k): (x, y) → (h + s(x-h), k + s(y-k))
A scale factor above 1 enlarges. A value between 0 and 1 shrinks.
How to Use This Calculator
- Enter one coordinate pair per line.
- Select the required transformation from the menu.
- Fill only the parameters needed for that rule.
- Press Transform Coordinates to generate the image points.
- Review the result table, centroid summary, and Plotly graph.
- Download the output as CSV or PDF when needed.
FAQs
1. What coordinate format does the calculator accept?
Enter one point per line as x,y or (x,y). Decimals and negative values work. Blank lines are ignored during processing.
2. Does a positive angle rotate clockwise?
No. Positive angles rotate counterclockwise. Use a negative angle if you want a clockwise rotation.
3. Can I transform many points at once?
Yes. Enter multiple coordinates, one per line. The calculator transforms every point and shows the full result table.
4. Why do reflections change signs?
A reflection flips points across a mirror line. The new signs depend on the selected line and the point position.
5. What happens with a negative dilation scale factor?
The figure still scales by the factor magnitude, but it also reverses through the chosen dilation center.
6. Why does area change after dilation?
Area scales by the square of the scale factor. Perimeter scales by the absolute value of the scale factor.
7. Can I rotate or dilate around a point other than the origin?
Yes. Choose the custom center option, then enter the center coordinates in the dedicated input fields.
8. Why are some values rounded in the results?
Rounded values improve readability. The tool still calculates using your entered numbers before displaying formatted results.