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Translations 3-1D

Translations 3-1D. What is the definition of a translation? What are some uses of translations? Is there a connection between translations and vectors?. Definition. A translation is a transformation that moves all the points in a plane a fixed distance in a given direction (slide).

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Translations 3-1D

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  1. Translations 3-1D What is the definition of a translation? What are some uses of translations? Is there a connection between translations and vectors?

  2. Definition A translation is a transformation that moves all the points in a plane a fixed distance in a given direction (slide).

  3. Translations The arrow shows the direction of the translation.

  4. Translation vector Since vectors have a distance and a direction, they are often used to describe translations. The vector shows the direction of the translation and its length gives the distance each point travels. To measure direction, add a horizontal dotted line and measure counterclockwise

  5. Find the translation image of each of the following using vector PQ P B • Point Y • Segment CD • Segment XZ • Triangle YXZ • Point D • Point L • Segment AB • Segment MN • Triangle LMN • Point B D A Q M C X L N Y Z

  6. Translate It page 172 P (2,4) 3 Vector <3,6> N 6 x’s 2−(−1) = 3 y’s 4−(−2) = 6 Q (−1,−2) M

  7. Try It The translation image of A (4, −2) is B (5,2). Give the translation vector and the coordinates of the image of C (−1,4). Translation vector is <1,4> 5 − 4 = 1 2 −(−2) = 4 C’ = (0,8) −1 + 1 = 0 4 + 4 = 8

  8. Translations change only the location of a figure. Translations preserve any property that has to do with the size of a figure including: • The lengths of its sides • The measure of its angles • The area and perimeter of the figure Translations also preserve the orientation of the figure.

  9. What is the definition of a translation? A translation is a transformation that moves all the points in a plane a fixed distance in a given direction. • What are some uses of translations? Patterns are created by translations. • Is there a connection between translations and vectors? Since vectors have a distance and a direction, they are often used to describe translations.

  10. Assignment 3-1D Page 173, 1-15 What is the translation vector for problems12-15?

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