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Geometry 1-7 Day 1

Geometry 1-7 Day 1. Transformations in the Coordinate Plane. Learning Targets. Students will be able… Identify reflections, rotations, and translations. Graph transformations in the coordinate plane. Warm-up. 1. Find the circumference and area of a circle with radius 5.

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Geometry 1-7 Day 1

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  1. Geometry 1-7 Day 1 Transformations in the Coordinate Plane

  2. Learning Targets • Students will be able… • Identify reflections, rotations, and translations. • Graph transformations in the coordinate plane.

  3. Warm-up 1. Find the circumference and area of a circle with radius 5. 2. Find the distance between point J and point T. J(7, 1) and T(-2, -4)

  4. Homework Check

  5. Homework Check

  6. Homework Check

  7. Homework Check

  8. Homework Check

  9. Go over Quiz

  10. Vocabulary • Transformation • A change in position, size, or shape of a figure. Does anyone know of a type of transformation?

  11. 3 Types of Transformations

  12. Reflection Construction • Fold your paper in half. Draw the line that is formed by the fold. • Label the fold “Line of Reflection” • Draw a triangle on one side of your paper. Label the vertices. • Place your Mira on the fold of your paper. • Look through the Mira to draw it’s reflection. Label the vertices as you see them in the Mira. * You have now constructed a Reflection. We will look at the characteristics that are present!

  13. Reflection Construction • Draw a line from A to A’. • Find the measure from A to the line of reflection. • Find the measure from A’ to the line of reflection. What do you notice? Equal Distance! You could continue this for B to B’ and C to C’

  14. Reflection Construction • What do you notice between your line drawn from A to A’ and the Line of Reflection? • Perpendicular • Now lets write the identification. Reflection,

  15. 3 Types of Transformations P

  16. Rotation Construction • Draw a rectangle or a triangle. (Go over it with a marker so you can really see it) • Label a point P outside of your figure. • This is your point of reflection • Take another sheet of paper and place it over the top of the figure. TRACE EVERYTHING (the figure and the point of reflection) • Place the copied figure underneath the original. Line up all points.

  17. Rotation Construction 5. Rotate the figure underneath the original. Make sure that point P is still lined up. 6. Redraw this figure labeling the new points with apostrophes. 7. Measure the distance from… C to P and C’ to P B to P and B’ to P A to P and A’ to P What do you notice?

  18. Rotations • When you can identify a specific degree of turn for a rotation you should write it. • For example rotation 90°, 180°, 270°

  19. 3 Types of Transformations P

  20. More Vocabulary • Preimage • The original figure. • Image • The figure after it is reflected, rotated or translated. • Has the apostrophes

  21. Examples • Preimage • Image B B’ A C’ C A’

  22. Notation Steps • Write the type of transformation. • Label the preimagefigure. • Write an arrow. • Label the image (label the same points in the same order just use an apostrophe ‘ ).

  23. Example

  24. Practice

  25. Example 1: Identify each transformation. Then use arrow notation to describe the transformation.

  26. Example 1: Identify each transformation. Then use arrow notation to describe the transformation.

  27. Example 1: Identify each transformation. Then use arrow notation to describe the transformation.

  28. Example 1: Identify each transformation. Then use arrow notation to describe the transformation.

  29. Example 2: Graph Paper Needed 1. A figure has vertices at A(-1, 4), B(-1, 1), and C(3, 1). After a transformation, the image of the figure has vertices at A’(-1, -4), B’(-1, -1), and C’(3, -1). Draw the preimage and image. Then identify the transformation. Reflection across the x-axis.

  30. Example 2: Graph Paper Needed 1. 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. Rotation, 90°

  31. Wrap-up • Without looking back at your notes who can tell me all three types of transformations?

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