3.14.1 Translation

In mathematics and geometry, transformations are operations that move, rotate, or change the shape of a figure. Some of the basic transformations include: 

Translation: 

A translation is a transformation that moves a figure in a straight line without changing its shape or orientation. 

• The figure moves a fixed distance in a specified direction.
• To perform a translation, you need to specify the distance and direction of the movement.
  • The distance is the amount by which each point of the figure moves, and the direction is the line or vector along which the figure moves.
•  The movement can be in any direction, including horizontally, vertically, or diagonally.
• A translation can be described using coordinates or vectors. 
• If the original figure has coordinates \((x,y)\), then its translated image will have coordinates
  • \((x + a, y + b)\), where a and b are the distances of the translation in the \(x\) and \(y\) directions, respectively.
• For example, if you want to translate a square by 2 units to the right and 3 units up, you would add 2 to the x coordinates of all its vertices and add 3 to their y coordinates. This will move the entire square 2 units to the right and 3 units up, without changing its shape or orientation.

Worked example:

Draw the image of shape A after a translation by the vector 8-6.

A translation is a transformation that moves a figure in a straight line without changing its shape or orientation.

The top number in the vector is 8, so move the shape A 8 units to its right.

The bottom number is -6, so move the shape A 6 units downward.