In math terms, translation is the process of moving a geometric shape without rotating or resizing it. This can be done by adding or subtracting a certain number from the coordinates of each point in the shape.

## Now take a closer look

Translation in math terms refers to the process of shifting the position of a geometric shape without rotating or resizing it in any way. This definition is often used in geometry and is an important concept to understand when working with shapes and space.

To perform a translation, a specific vector must be added or subtracted from the coordinates of each point in the shape. This vector determines the direction and distance of the translation. The resulting shape will have the same proportions and angles as the original, but will appear to have been moved to a new location.

A famous quote related to this concept comes from Carl Friedrich Gauss, a 19th-century mathematician who said, “Mathematics is the queen of sciences, and geometry is the queen of mathematics.”

Here are some interesting facts about translation in math:

- In addition to translations, there are two other common types of transformations in geometry: rotations and reflections.
- Translations are often performed using coordinate notation, which involves writing the coordinates of each point as ordered pairs and then adding or subtracting a set of values to these pairs.
- If a shape is translated multiple times, the resulting shape is called a composition of translations.
- Translations are a fundamental concept in computer graphics, where they are used to move objects around on a screen.
- A translation can be represented graphically with an arrow that shows the direction and magnitude of the shift. Here’s an example of a translation of a triangle:

Original triangle | Translated triangle |
---|---|

(0,0) | (4,3) |

(3,0) | (7,3) |

(0,2) | (4,5) |

Overall, translation is an important concept in math and geometry that helps us understand how shapes can be moved around in space. By understanding translations, we can better understand many other geometrical concepts and apply them in real-world situations.

## Video response to your question

This YouTube video provides a definition of translation in math, specifically in geometry. It explains that translation is a function that moves an object a certain distance, with every point of the object being moved in the same direction and by the same distance, without altering the object’s size, rotation, or reflection. The video also discusses various ways in which information about translation may be presented, such as a figure on the coordinate plane or a description in mathematical notation. The initial object is referred to as the pre-image and the object after the translation is called the image.

**Further responses to your query**

A translation is a type of transformation that takes each point in a figure and slides it the same distance in the same direction.

## In addition, people are interested

*a transformation that moves every point in a figure the same distance in the same direction*. For example, this transformation moves the parallelogram to the right 5 units and up 3 units. It is written ( x , y ) → ( x + 5 , y + 3 ) .

*the process of converting the meaning of a written message (text) from one language to another*.

*of*a figure

*in*a point, a line, or a plane.

*Translation*: transformation that moves all points

*of*a figure

*the*same distance

*in the*same direction. Show Video Lesson. Try

*the*free Mathway calculator and problem solver below to practice various

*math*topics.

## Fascinating Facts

**Thematic fact:**This means that a translation is an isometric transformation which means that the preimage and image are congruent figures, as ck-12 accurately states. So how do we represent translations mathematically? We use vectors to represent a translation. Which means we need direction (up, down, left, or right) and magnitude (length of units).

**And did you know that,**An object that looks the same before and after translation is said to have translational symmetry. A common example is a periodic function, which is an eigenfunction of a translation operator. Wikimedia Commons has media related to Translation (geometry).

**Did you know that,**In translation notation, the first number represents how many units in the x direction, the second number, how many in the y direction. Both numbers tell us about how far and in what direction we are going to slide the point.