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1-7 Geometry

1-7 Geometry. Transformations in the Coordinate Plane. Learning Targets. Students will be able… Identify reflections, rotations, and translations. Graph transformations in the coordinate plane. Warm-up. Homework Check. Homework Check. Homework Check. Homework Check.

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1-7 Geometry

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  1. 1-7 Geometry 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

  4. Homework Check

  5. Homework Check

  6. Homework Check

  7. Homework Check

  8. Translations in the Coordinate Plane 1. Find the coordinates for the image of after the translation (x, y) (x + 3, y – 4). A(-1, 1), B(-3, 3), and C(-4, 0). Draw the preimage and then find the image and label points A’, B’, and C’. (x, y) ( x + 3 , y – 4 ) A(-1, 1) A’( , ) B(-3, 3) B’ ( , ) C(-4, 0) C’( , )

  9. Translations in the Coordinate Plane 2. Find the coordinates for the image JKLM after the translation (x, y) (x – 2, y + 4) When J(1, 1), K(3, 1), L(3, -4), and M(1, -4). Draw the preimage and image. (x, y) ( x – 2 , y + 4 ) J(1, 1) J’( , ) K(3, 1) K’ ( , ) L(3, -4) L’( , ) M(1, -4) M’( , )

  10. Standing Translations Start in the middle of the room. Take different steps for the appropriate transformations. We should all move as a class.

  11. Standing Translations (x, y) ( x + 1 , y – 3 ) (x, y) ( x – 2 , y – 4 ) (x, y) ( x + 0 , y + 1 ) (x, y) ( x – 1 , y + 2 )

  12. Transformation Review and Practice 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.

  13. Transformation Review and Practice 2. Triangle ABC has points A(-1, 1) B(-1, 3) and C(1, 2). It’s image has points A’(-1, -1), B’(-3, -1) and C’(-2, 1). Identify the transformation, then use arrow notation to describe the transformation.

  14. Transformation Review and Practice 3. Square DEFG has points D(-4, 2), E(-1, 2), F(-1, 2), and G(-4, 1). It’s image has points D’(-4, -2), E’(-1, -2), F’(-1, -1), and G’(-4, -1). Identify the transformation, then use arrow notation to describe the transformation.

  15. Transformation Review and Practice 4. Given points P(-2, -1) and Q(-1, 3). Draw and its reflection across the y-axis.

  16. Transformations Review and Practice 5. Find the coordinates of the image F(2, 7) after the translation (x, y) (x + 5, y – 6). Draw and label the image.

  17. Transformations Review And Practice 6. Find the coordinates of the image A(1, 3), B(4 -5) and C(-1, -1) after the translation (x, y) (x - 2, y + 3). Draw and label the image.

  18. 1-7 Worksheet Complete the sentence. 1. A __________________ is the movement of a figure from its original position to a new position. 2. The _________________ position is called the preimage. The new position is called the _________________. 3. A __________________ (or flip) is a transformation across a line. 4. A translation (or ___________) is a transformation in which all the points of a figure move the same distance in the same direction. 5. A ____________________ (or turn) is a transformation about a point.

  19. 1-7 Worksheet Match the picture below with the type of transformation below with the appropriate picture. Then use arrow notation to describe the transformation. 6. Rotation ____ Arrow notation ______________ 7. Reflection ___ Arrow Notation ______________ 8. Translation ___ Arrow Notation ______________

  20. 1-7 Worksheet 9. A figure has vertices at D(-2, 1), E(-3, 3), and F(0, 3). After a transformation, the image of the figure has vertices at D’(-1, -2), E’(-3, -3), and F’(-3, 0). Draw the preimage and the image. Then identify the transformation.

  21. 1-7 Worksheet 10. A figure has vertices at (5, 5), (2, 6), (1, 5), and (2, 4). After a transformation, the image of the figure has vertices at (5, 5), (6, 8), (5, 9), and (4. 8). Draw the preimage and image. Then describe the transformation.

  22. 1-7 Worksheet 11. The coordinates of the vertices of quadrilateral DEFG are (3, 0), (2, 3), (-3, 2), and (-2, -1). Find the coordinates for the image of rectangle DEFG after the translation (x, y) (x + 4, y – 3) (x, y)  (x + 4, y – 3) (3, 0)  (2, 3)  (-3, 2)  (-2, -1) 

  23. Wrap-up

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