Enter point and translation values
Example data table
| Mode | Original Point | Translation Vector | Translated Point | Movement Magnitude |
|---|---|---|---|---|
| 2D | (2, 3) | <4, -1> | (6, 2) | 4.12 |
| 2D | (-5, 7) | <3, 2> | (-2, 9) | 3.61 |
| 2D | (0, -4) | <-6, 5> | (-6, 1) | 7.81 |
| 3D | (1, 2, 3) | <4, -2, 5> | (5, 0, 8) | 6.71 |
| 3D | (-2, 6, -1) | <3, 1, -4> | (1, 7, -5) | 5.10 |
Formula used
2D translation formula
x′ = x + Δx
y′ = y + Δy
3D translation formula
x′ = x + Δx
y′ = y + Δy
z′ = z + Δz
Vector notation
If a point moves by vector <a, b>, then (x, y) becomes (x + a, y + b). In 3D, use <a, b, c> and update all three coordinates.
Movement magnitude
For 2D, magnitude = √(Δx² + Δy²). For 3D, magnitude = √(Δx² + Δy² + Δz²). This shows how far the point traveled during translation.
Homogeneous matrix view
Advanced courses often represent translation using homogeneous coordinates. In 2D, translation can be handled with a 3×3 matrix. In 3D, it uses a 4×4 matrix. The coordinate shift is identical to the formulas above.
How to use this calculator
- Select either 2D or 3D mode.
- Enter the original point coordinates.
- Enter the translation amounts for each axis.
- Choose the display precision you want.
- Press Calculate Translation.
- Read the translated point, notation, metrics, and graph shown above the form.
- Use the CSV button to save a spreadsheet-friendly result.
- Use the PDF button to export a printable summary.
Frequently asked questions
1. What does translating a point mean?
Translation moves a point by fixed amounts along one or more axes. The shape and orientation stay unchanged. Only the location shifts.
2. Does translation change the distance between points in a figure?
No. Translation is a rigid motion. Distances, angles, and shape size remain exactly the same after every point shifts by the same vector.
3. Can this calculator handle negative translations?
Yes. Negative values move the point in the opposite direction of the positive axis. For example, a negative Δx shifts left.
4. What is the difference between 2D and 3D translation?
2D translation updates x and y only. 3D translation updates x, y, and z. The same addition rule applies in both cases.
5. Why is the movement magnitude useful?
It measures the straight-line distance traveled during the translation. This helps in geometry, physics visuals, animation paths, and coordinate checks.
6. Does the calculator show where the point started and ended?
Yes. It reports both coordinates, identifies the quadrant or octant, and shows the full translation notation for the move.
7. Can I use decimal values and fractions?
Yes. Decimal values work directly. Fractions can be entered as decimal equivalents, such as 0.5 for one-half or 1.25 for five-fourths.
8. Why does the result section appear above the form?
That layout makes the newest answer visible immediately after submission. It reduces scrolling and keeps the chart, exports, and summary easy to access.