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**Getting Started… 9.6 - Translations**

Find y (figure not drawn to scale!): 139º 5yº 71º 9yº 92º Y = 17

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**The action of sliding a figure in any direction.**

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

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Translation The act of sliding a figure in any direction.

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**Reflection (flip - mirror)**

The result of a figure flipped over a line.

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Reflection The result of a figure flipped over a line.

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**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.

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**Turning a figure around a point or a vertex**

Rotation

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**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

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

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**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)

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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)

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**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

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**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

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**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

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**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

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**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

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**Last One What is the equation of this line? Name an equation of**

a line that is translated vertically 3 units up?

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**Homework Extra Practice 9.6**

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Translations and Reflections. Move the figure Same shape and size (Congruent) (x ± n, y ± m) x + n, move every point n units to the right x –

Translations and Reflections. Move the figure Same shape and size (Congruent) (x ± n, y ± m) x + n, move every point n units to the right x –

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