# TRANSLATIONS

### Lindsey Green & Faith Najfus

## What is a translation?

A translation is a transformation of a plane that slides every point of a figure the same distance in the same direction. A translation creates a figure that is congruent with the original figure and preserves distance and orientation.

## Function Rules

T(x, y) = (x + h, y + k) To use the function rule you are going to add the vector, or h & k or T, to your preexisting points x & y. Your h is what you're adding to the x and your k is what your adding to the y.

## Example This is a basic example of a translation showing that all of the points moved the same distance in the same direction. | ## Example 2 This example shows a translation of 7,4. Because these coordinates are positive, they will be added to the original coordinates instead of subtracting them. As shown, point c has the original coordinates of (-2,3). When the translation is completed the new C' point is (5,7). | ## Example 3 This last example is something you would normally see when solving translations. It includes the original triangle and the translated triangle, but it does not include the translation. To find the translation you need to figure out if the original x and y coordinates are being added or subtracted. If added, the translation would be positive and if subtracted, it would be a negative translation. In this case, the x variable has a negative translation and the y value has a positive translation. This was found by counting the spaces between an original coordinate and a translated coordinate. The spaces came out to be a translation of -5,2. To check all of the coordinates to make sure this is the right translation you have to use the function notation, T -5,2 (x,y)= x-5 y+2(imagine -5,2 as a subscript). Plug each of the original coordinates into the x & y and solve. Your answers will be the translated coordinates. |

## Example

This is a basic example of a translation showing that all of the points moved the same distance in the same direction.

## Example 2

This example shows a translation of 7,4. Because these coordinates are positive, they will be added to the original coordinates instead of subtracting them. As shown, point c has the original coordinates of (-2,3). When the translation is completed the new C' point is (5,7).

## Example 3

This last example is something you would normally see when solving translations. It includes the original triangle and the translated triangle, but it does not include the translation. To find the translation you need to figure out if the original x and y coordinates are being added or subtracted. If added, the translation would be positive and if subtracted, it would be a negative translation. In this case, the x variable has a negative translation and the y value has a positive translation. This was found by counting the spaces between an original coordinate and a translated coordinate. The spaces came out to be a translation of -5,2. To check all of the coordinates to make sure this is the right translation you have to use the function notation,

T -5,2 (x,y)= x-5 y+2(imagine -5,2 as a subscript). Plug each of the original coordinates into the x & y and solve. Your answers will be the translated coordinates.

## Sources

Accelerated math textbook pages 459-465

www.regentsprep.org/regents/math/geometry/gt2/Trans.htm

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