Translation Calculator. Enter your object type (point, line, or polygon), define its coordinates, and specify a translation vector (X, Y) to shift it across the 2D plane. The Translation Calculator applies the vector to every point and returns the translated coordinates instantly — perfect for geometry homework, game dev, or visualizing transformations. Also try the Distance Calculator (3D).
A geometric translation is a transformation that moves every point of a figure the same distance in the same direction, defined by a translation vector (x, y). The shape, size, and orientation of the object remain unchanged — it simply slides to a new position on the coordinate plane. See also our calculate Ratios of Directed Line Segments.
To translate a point (a, b) by vector (x, y), simply add the vector components to the coordinates: the new point is (a + x, b + y). For example, translating (3, 4) by vector (2, -1) gives the new point (5, 3).
No. Translation is a rigid transformation (also called an isometry), which means it preserves distances, angles, and the overall shape and size of the object. Only the position changes.
To translate a line segment, apply the translation vector to both endpoints independently. The resulting line segment is parallel to the original and has the same length — it has simply shifted position.
Translate each vertex of the polygon using the same translation vector. Add the vector's X component to each vertex's X coordinate and the vector's Y component to each vertex's Y coordinate. The translated polygon will be congruent to the original.
The displacement magnitude is the straight-line distance between the original position and the translated position, calculated as √(vectorX² + vectorY²). It tells you exactly how far the object has moved, regardless of direction.
Yes. A negative X component shifts the object to the left, and a negative Y component shifts it downward. Positive values shift right and upward respectively. You can combine any positive or negative values to move the object in any direction.
Enter your polygon vertices as space-separated coordinate pairs in the format: x1,y1 x2,y2 x3,y3 and so on. For example, a rectangle might be entered as 0,0 4,0 4,3 0,3. The calculator will translate each vertex by the given vector. You might also find our find Slope Percentage with Slope Percentage Calculator useful.