Translation Calculator
Translate a point by a displacement vector (dx, dy) and return the image coordinates.
About Translation Calculator
Translation shifts every point by the same displacement vector (dx, dy). The image point is (x+dx, y+dy). Translation preserves shape, size, and orientation.
Formula
Translation
(x', y') = (x + dx, y + dy)
- x,y
- Original point
- dx,dy
- Displacement vector
Worked example
With the default values below, Translation Calculator returns Image X of 7.0000. Change any input above and every figure here is recalculated in your browser.
Inputs used
- Point x
- 2
- Point y
- 3
- dx (horizontal shift)
- 5
- dy (vertical shift)
- -2
Results
- Image X
- 7.0000
- Image Y
- 1.0000
Step by step
- 1Apply translation= (7, 1)
Assumptions and limits
- The result is derived only from the 4 inputs listed above. Anything not among them is not part of the calculation.
- In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
- Figures are rounded for display to 4 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.
How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.
Frequently Asked Questions
Does translation change the shape?
No — translation is a rigid motion. It moves all points the same distance in the same direction without rotating or resizing.
How do I reverse a translation?
Apply the opposite vector: (−dx, −dy).