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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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Properties of Reflections. Warm up Triangle ABC has vertices A(1, 1), B(3, 1), and C(2, 4). Describe how each reflection changes the coordinates of the.

Properties of Reflections. Warm up Triangle ABC has vertices A(1, 1), B(3, 1), and C(2, 4). Describe how each reflection changes the coordinates of the.

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