translação

Translating an object in geometry refers to moving every point of the object by the same distance in the same direction. This movement is known as a translation vector. Imagine sliding a shape across a surface without rotating or flipping it. The original position of the object is called the pre-image, and its new position after the translation is called the image. Every point on the pre-image is displaced by the exact same amount and in the same direction to arrive at its corresponding point on the image. This means that the size, shape, and orientation of the object remain unchanged after a translation. It is a rigid transformation, preserving distances between points and angles within the object. In the coordinate plane, a translation can be represented by adding the components of the translation vector to the coordinates of each point of the object. For example, translating a point (x, y) by a vector (a, b) results in a new point (x+a, y+b). This concept is fundamental in various areas of mathematics, including geometry, computer graphics, and physics.