9.2 - Translations By: Hailey Wilson

What are Translations?

• A Translation is a function that maps each point to its image along a vector, it is also known as a translation vector

• A translation vector is a transformation that moves all points of a figure to the same distance in the same direction

A Translation is also known as a slide, in which the Translation can slide either Up (add to y), Down (subtract from y), Left (subtract from x) or Right (add to x)

EXAMPLE 1: Draw a Translation

Determine the translation of triangle XYZ to vector W

Step 1: Determine the length of vector W and locate where point X lies, draw a parallel vector along point X

Step 2: Next, determine the location of the next two points and draw their vectors parallel to vector W

Step 3: Conect the vertices and points to form the translated image along the parallel vectors

Example 2: Translations in the Coordinate Plane

*To translate a point along a vector (a, b), add a to the x-coordinate and b to the y-coordinate*

(x, y) —> (x + a, y + b)

Triangle EFG with ventricles E(-7, -1), F(-4, -4), and G(-3, -1); (2, 5)

(2, 5) —> Up 2 and Right 5

(x, y) —> (x + 2, y + 5)

E(-7, -1) —> E(-7 + 2, -1 + 5) —> E(-5, 4)

F(-4, -4) —> F(-4 + 2, -4 + 5) —> F(-2, 1)

G(-3, -1) —> G(-3 + 2, -1 + 5) —> G(-1, 4)

Credits:

Created with images by Brett Jordan - "Triangles #9" • Brett Jordan - "Triangles #9" • Brett Jordan - "Triangles #9" • Brett Jordan - "Triangles #9" • Brett Jordan - "Triangles #9" • Brett Jordan - "Triangles #9" • Brett Jordan - "Triangles #9" • Brett Jordan - "Triangles #9" • Brett Jordan - "Triangles #9" • Brett Jordan - "Triangles #9" • Brett Jordan - "Triangles #9"

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