9.1 Translate Figure and Use Vectors Translations anslation.swf&w=894&h=762&col=%23FFFFFF&title=Geometry+Tr anslation Vector/Translations Rotations rotational symmetry

Translation same size same shape A translation moves a figure to a new location.

For all Transformations (including Translations) New figure is called an _____________. Original figure is called a _____________.image pre-image

Translate a figure in the coordinate plane Example 1:Graph quadrilateral ABCD with vertices A(-1, 2), B(-1, 5), C(4, 6), and D(4, 3). Find the image of each vertex after the translation (x, y) → (x + 3, y – 3). Then graph the image using prime notation.

Types of Transformations (Preview- DON’T Write down) Translation Reflection Rotation Dilation are all Isometries If a transformation is an Isometry, then the image is the same shape and size of it’s pre-image.

Write a translation rule and verify congruence Write a rule for the transformations of ∆ ABC to ∆ A’B’C’. Then verify whether or not each transformation is an isometry. If so, use a congruence postulate (SAS, ASA, SSS, AAS). a)b)

VECTORS A vector is a quantity that has both _______________ and ______________________, or size. It is used as another way to describe a _______________________________. A vector is represented in the coordinate plane by an _______________ drawn from one point to another. direction magnitude translation ray

F G  5,3   5,3 

Identify vector components Example 3:Name the vector and write its component form.  5, -2   -7, 0 

EXAMPLE 4: The vertices of ∆ABC are A(0, 3), B(2, 4), and C(1, 0). Translate ∆ABC using the vector 5,-1.

Example 5: The vertices of ∆ABC are A(-1, -1), B(0, 2), and C(1, 0). Translate ∆ABC using the vector.