Getting Started… Translations

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Getting Started… 9.6 - Translations
Find y (figure not drawn to scale!): 139º 5yº 71º 9yº 92º Y = 17

The action of sliding a figure in any direction.
Translation (Slide) The action of sliding a figure in any direction.

Translation The act of sliding a figure in any direction.

Reflection (flip - mirror)
The result of a figure flipped over a line.

Reflection The result of a figure flipped over a line.

The action of turning a figure around a point or a vertex.
Rotation (Turn) The action of turning a figure around a point or a vertex.

Turning a figure around a point or a vertex
Rotation

Terminology B B’ Horizontal Translation A A’
Image – final image after transformation Labeled with “Prime” Pre-image – image before transformation Labeled with Capital Letters B B’ Horizontal Translation A A’ Pre-Image Image

Translation A Image Pre-Image Slide Arrow C B A’ B’ C’

Algebraic Translations
Let B have coordinates (2,5). Find the image of B after the following translation: Left 4 units , up 2 units: Right 5 units, down 9 units: (-2, 7) (7, -4)

Try some more! Let point C have the coordinates (-4,1). Find the image coordinates C for each translation. - (x,y)  (x + 3, y – 1) -(x,y)  (x – 2, y + 5) (-1, 0) (-6, 6)

Find the image coordinates for each translation(x, y) → (x-5, y)
4 3 2 1 -5 -4 -3 -2 -1 B B A C C A

Find the image coordinates for each translation
5 4 3 2 1 -5 -4 -3 -2 -1 Find the image coordinates for each translation (x, y) → (x-1, y + 3) B A D C B A C D

Triangle ABC has vertices A(–2, 1), B(2, 4), and C(1, 1).
Find the coordinates of the vertices of the image if it is translated 3 units to the right and 5 units down. Answer: The coordinates of the vertices of the image are A(1, –4), B(5, –1), and C(4, –4). Example 2-3a

Graph triangle ABC and its image.
Answer: B The preimage is . A(–2, 1), B(2, 4), and C(1, 1). A C B The translated image is A(1, -4), B(5, -1), and C(-4, -4). A C Example 2-3b

Triangle JKL has vertices J(2, –3), K(4, 0), and L(6, –3).
a. Find the coordinates of the vertices of the image if it is translated 5 units to the left and 2 units up. b. Graph triangle JKL and its image. Answer: J(–3, –1), K(–1, 2), L(1, –1) Answer: Example 2-3c

Last One  What is the equation of this line? Name an equation of
a line that is translated vertically 3 units up?

Homework Extra Practice 9.6

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