Point Translation Calculator

Visualize and calculate the translation of points in 2D and 3D space.

Enter Coordinates

Point P (x, y) or (x, y, z):

Translation Vector (dx, dy) or (dx, dy, dz):

Translated Point P' Coordinates:

Visualization

Understanding Point Translation

In geometry, translation moves every point of a shape or space by the same distance in a given direction. It's like sliding a figure without rotating or resizing it. To translate a point, you simply add the components of the translation vector to the coordinates of the point.

Formula:

For a point P(x, y) and a translation vector V(dx, dy), the translated point P'(x', y') is calculated as:

x' = x + dx
y' = y + dy

Similarly, in 3D space, for a point P(x, y, z) and a vector V(dx, dy, dz), the translated point P'(x', y', z') is:

x' = x + dx
y' = y + dy
z' = z + dz

Use Cases:

Point translation is fundamental in computer graphics, robotics, and physics simulations. It's used in moving objects on screen, calculating robot movements, and simulating physical displacements.

Sources: Wikipedia - Translation (geometry)