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Getting Started… 9.6 - Translations Find y (figure not drawn to scale!): 5yº 9yº92º 139º 71º Y = 17

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

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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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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

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

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Translation Pre-ImageImage Slide Arrow A B C 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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5 4 3 2 1 -5-4-3-2 12345 -2 -3 -4 -5 Find the image coordinates for each translation(x, y) → (x-5, y) A B C B A C

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5 4 3 2 1 -5-4-3-2 12345 -2 -3 -4 -5 Find the image coordinates for each translation (x, y) → (x-1, y + 3) AB C D B A C D

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Example 2-3a 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).

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

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Example 2-3c 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:

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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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http://www.shodor.org /interactivate/activities /Transmographer/

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Homework Extra Practice 9.6

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