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Transformations in the Coordinate Plane

Learn about reflections, rotations, and translations in the coordinate plane. Understand the vocabulary and notation used to describe transformations. Practice identifying and drawing images of figures after transformations.

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Transformations in the Coordinate Plane

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  1. Objectives Identify reflections, rotations, and translations. Graph transformations in the coordinate plane.

  2. Vocabulary transformation reflection preimage rotation image translation

  3. _____________- change in the position, size, or shape of a figure. _____________- The original figure. _____________ The resulting figure. A transformation _____________ the preimage to the image. Arrow notation () is used to describe a transformation, and primes (’) are used to label the image.

  4. Example 1A: Identify the transformation. Then use arrow notation to describe the transformation.

  5. Example 1B: Identify the transformation. Then use arrow notation to describe the transformation.

  6. Example 2: A figure has vertices at A(1, –1), B(2, 3), and C(4, –2). After a transformation, the image of the figure has vertices at A'(–1, –1), B'(–2, 3), and C'(–4, –2). Draw the preimage and image. Then identify the transformation.

  7. To find coordinates for the image of a figure in a translation, add ato the _-coordinates of the preimage and add bto the _-coordinates of the preimage. Translations can also be described by a rule such as (x, y)  (x + _, y + _).

  8. Example 3: Find the coordinates for the image of ∆ABC after the translation (x, y)  (x + 2, y - 1). Draw the image.

  9. A’ Example 4: Use the diagram to write a rule for the translation of square 1 to square 3.

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