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Chapter 1

Chapter 1. 1-7 transformations on the coordinate plane. Objectives. Students will be able to: Identify reflections, rotations, and translations. Graph transformations in the coordinate plane. What is a transformation?.

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Chapter 1

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  1. Chapter 1 1-7 transformations on the coordinate plane

  2. Objectives • Students will be able to: • Identify reflections, rotations, and translations. • Graph transformations in the coordinate plane.

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

  4. Types of transformations

  5. Reflections • Types of reflections: • Reflection across the y-axis • Reflection across the x-axis • Reflection across a specific line

  6. Example #1 • Work on reflection worksheet problems 1-3

  7. Rotation • Definition of Rotation • A Rotation is a transformation that turns a figure about a fixed point. • More about Rotation • Rotation is also called as turn. • The fixed point around which a figure is rotated is called as centre of rotation.

  8. Example#2 • Lets work on problems 1-3 on rotation worksheet

  9. Translation • Moving a shape, without rotating or flipping it. "Sliding". • The shape still looks exactly the same, just in a different place. To Translate a shape:

  10. Example#3 • Do worksheet translation problem 1-3

  11. Identifying transformations • Identify the transformation. Then use arrow notation to describe the transformation. • 90° rotation, ∆ABC ∆A’B’C’

  12. Example#4 • Identify the transformation. Then use arrow notation to describe the transformation. • reflection, DEFG D’E’F’G’

  13. Drawing Transformation • 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. • The transformation is a reflection across the y-axis because each point and its image are the same distance from the y-axis.

  14. Example#5 • A figure has vertices at E(2, 0), F(2, -1), G(5, -1), and H(5, 0). After a transformation, the image of the figure has vertices at E’(0, 2), F’(1, 2), G’(1, 5), and H’(0, 5). Draw the preimage and image. Then identify the transformation. • The transformation is a 90° counterclockwise rotation.

  15. Homework • Lets work on all transformation worksheet problems 1-8

  16. Closure • Today we learn about transformations and how they work on the coordinate plane. • Next class we are going to continue with chapter 2

  17. Have a great day

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