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Translations

Translations. Section 9.1. Isometry. An isometry is a transformation that preserves length and angle measure. Types of isometries Translations Reflections Rotations . Transformation. A transformation moves or changes a figure in some way to produce a new figure called an image.

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Translations

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  1. Translations Section 9.1

  2. Isometry • An isometry is a transformation that preserves length and angle measure. • Types of isometries • Translations • Reflections • Rotations

  3. Transformation • A transformation moves or changes a figure in some way to produce a new figure called an image. • Another name for the original figure is the preimage.

  4. Image/Preimage • Every point in the original figure, preimage, is denoted with a capital letter (Ex: P, Q, R), while every point in the image is denoted with a capital letter followed by an apostrophe (Ex: P’, Q’, R’, read “P prime”, “Q prime”, “R prime”)

  5. Translation • A translation moves every point of a figure the same distance in the same direction. • Coordinate notation is denoted by (x,y)→(x + a, y + b) where a and b are numbers.

  6. Translations • Quadrilateral ABCD has vertices A(-1, 2), B(-1, 5), C(4, 6), and D(4, 2). Find the image of each vertex after the translation (x, y)→(x + 3, y – 1).

  7. Vector • Another way to describe a translation is by using a vector. A vector is a quantity that has both direction and magnitude. • The component form of a vector combines the horizontal and vertical components. The component form of FG is

  8. Vectors • The vertices of triangle ABC are A(0, 3), B(2, 4), and C(1, 0). Translate triangle ABC using the vector . • This is the same as using the translation (x, y)→(x + 5, y – 1)

  9. Translate the following • The vertices of triangle LMN are L(2, 2), M(5, 3), and N(9, 1). Translate the vertices by: • (x, y)→(x – 5, y + 3)

  10. Assignment • Pg. 576 #3-21

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