Perform translations

The  exercise appears under the 8th Grade Math Mission. This exercise presents the geometric transformation of translation.

Types of Problems
There are two types of problems in this exercise:


 * 1) Move the shape in the direction specified: This problem provides a grid with an orange polygon and a translation direction. The student is asked to use the manipulative to move the polygon as requested.Top1.png
 * 2) Define the translation that moves the shape as drawn: This problem provides a grid with an orange pre-image and a blue image. The student is asked to define the translation that moves the orange polygon onto the blue.Top2.png

Strategies
An ability to read the coordinate plane and knowledge of the notation for translations are all that is needed to perform this problem accurately and efficiently.
 * 1) A translation T(x,y) represents a translation moving x-units right and y-units left.
 * 2) When x is negative move left, when y is negative move down.

Real-life applications

 * 1) Translations can be viewed as vectors which are used in physics and linear algebra.
 * 2) A translation is an isometry (in particular a conformal map) which is useful for defining non-Euclidean geometries such as the possible hyperbolic geometry of space.