Geometry

4.1 Translations

Unit 2: Geometry ​

Transformation

​A FUNCTION that moves or changes a figure in some way.

It changes a PRE-IMAGE (ABC) into an IMAGE (A'B'C').

​Vector

Multiple Choice

In the diagram, name the vector and write its component form

• $$\overrightarrow{JK}$$

  <4, 3>

• $$\overrightarrow{JK}$$

  <3, 4>

• $$\overleftarrow{JK}$$

  <4, 3>

• $$\overrightarrow{JK}$$

  <-3, 4>

Graphing

The vertices of ABC are A (0, 3), B(2, 4), and C(1, 0).

Translate the triangle using the vector <5, -1> and plot the image, A'B'C'.

Translation Notation

You can also write translations using notation (math) by using the form above! It would be the same as the vector <a, b>.

Multiple Choice

Which of the following is the correct translation notation for the pre-image and image shown?

• <4, 1>

• <-4, 1>

• $$\left(x,\ y\right)\rightarrow\left(x-4,\ y+1\right)$$

• $$\left(x,\ y\right)\rightarrow\left(x+4,\ y-1\right)$$

Graphing

Graph quadrilateral ABCD with vertices A(−1, 2), B(−1, 5), C(4, 6), and D(4, 2) and its image after the translation (x, y) → (x + 3, y − 1).

​RIGID MOTIONS are also called ISOMETRIES

​The following transformations are rigid motions:
TRANSLATIONS
REFLECTIONS
ROTATIONS

RIGID MOTIONS
PRESERVE SHAPE AND SIZE

COMPOSITE of TRANSFORMATIONS

​You can perform more than one transformation

Multiple Select

Select all of the translations performed in this composite transformation.

• 
  $$\left(x,\ y\right)\rightarrow\left(x-5,\ \ y+2\right)$$

• <5, -2>

• $$\left(x,\ y\right)\rightarrow\left(x-4,\ y-2\right)$$

• <4, 2>