What is a geometric translation?
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 Shoelace Formula Calculator.
How do you translate a point by a vector?
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).
Does translation change the shape or size of an object?
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.
How do you translate a line segment?
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. You might also find our Distance Calculator (3D) useful.
How do you translate a polygon?
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.
What does the displacement magnitude represent?
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.
Can the translation vector have negative values?
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.
How do I enter polygon points in this calculator?
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.