Shape & Space Part C: Transformations

Transcription

1 Name: Homeroom: Shape & Space Part C: Transformations Student Learning Expectations Outcomes: I can describe and analyze position and motion of objects and shapes by Checking for Understanding identifying and plotting points in the first quadrant of a Cartesian plane, using whole number ordered pairs. performing a combination of translations, rotations and/or reflections on a single 2-D shape, with and without technology, and draw and describe the image. performing a combination of successive transformations of 2-D shapes to create a design, and identify and describe the transformations. performing and describing single transformations of a 2-D shape in the first quadrant of a Cartesian plane (limited to whole number vertices).

2 Coordinate Pairs 1. Plot the following ordered pairs A (0, 4) B (6, 14) C (12, 0) D (8,2) E (8, 14) F(14,14) G(14,2) H (2,0) I (6,12) J (12,12) K (12,0) Connect A to B to C back to A. What shape is created? Connect D to E to F to G back to D. What shape is created? Connect H to I to J to K back to H. What shape is created? Plot 6 points to create a hexagon. Label and write the coordinated of all your points. A B C D E F 2

3 I can identify and plot points in the first quadrant of a Cartesian plane, using whole number ordered pairs. 1. Write the coordinates of the vertices of each shape. a) b) c) 2. Find the length of each line segment on this coordinate grid. Describe the strategy you used. 3

4 3. Draw and label a coordinate grid. a) Plot each point on the grid. What scale will you use? Explain your choice. A(5, 5) B(10, 15) C(10, 25) D(20, 20) E(20, 10) b) Join the points in order. Then join E to A. Describe the shape you have drawn. 4. Draw and label a coordinate grid. a) Plot each point on the grid. What scale will you use? Explain your choice. P(4, 0) Q(2, 8) R(6, 12) S(8, 6) T(12, 8) U(8, 2) b) Join the points in order. Then join U to P. Describe the shape you have drawn. 4

5 Translations 1. Draw a quadrilateral and tell what are the coordinates of the vertices of quadrilateral ABCD? 2. Quadrilateral ABCD is translated 2 units up and 4 units left. What are the coordinates of the vertices of the image? 3. Draw a triangle and tell what are the coordinates of the vertices of EFG? 4. If triangle EFG is translated 5 units down and 3 units right, what are the coordinates of the vertices of the image? 5

6 Name Reflections Date 1. On the coordinate grid below, draw and label a triangle with vertices X(6, 1), Y(4, 5), and Z(2, 1). a) Draw X'Y'Z' after a reflection in the 6 x-axis. You may want to extend your graph to perform the reflection. b) What are the coordinates of the vertices of X'Y'Z'? X', Y', Z' 6

7 Rotations 1. Describe the combination of transformations that move parallelogram ABCD onto its image, parallelogram A'B'C'D'. 2. Draw the transformed image that will: a) Rotate triangle ABC 90 degrees counter clockwise along point C. b) Now reflect the image along the horizontal line created by connecting point (2,2) to (8,2) c) Finally, translate the image 3 units up and 2 units right. 7

8 I can perform a combination of translations, rotations and/or reflections on a single 2-D shape, with and without technology, and draw and describe the image. 1. Copy this triangle on a grid. a) Draw the image of EFG after a reflection in the line of reflection. b) Write the coordinates of the vertices of the triangle and its image. Describe how the positions of the vertices have changed. c) Another point on this grid is H(5, 3). Predict the location of H' after a reflection in the same line. How did you make your prediction? 2. This diagram shows a shape and its image after 3 different transformations. Identify each transformation. Explain how you know. a) the shape to Image A b) the shape to Image B c) the shape to Image C 3. A quadrilateral has these vertices. Draw the quadrilateral on a coordinate grid. U(0, 3) V(0, 6) W(3, 5) X(4, 3) Draw the image of the quadrilateral after each transformation: a) a translation of 2 squares right and 3 squares up b) a reflection in the horizontal line through the vertical axis at 3 c) a rotation of 90 clockwise about vertex X 8

9 I can perform a combination of translations, rotations and/or reflections on a single 2-D shape, with and without technology, and draw and describe the image. 1. a) Copy the pentagon on grid paper. Translate the pentagon 1 square left and 5 squares down. Then rotate the translation image 90 counterclockwise about point R. b) Draw and label both images. c) What can you say about the pentagon and its final image? How can you check? 2. a) Copy the triangle on a coordinate grid. Reflect the triangle in the horizontal line through 4 on the vertical axis. Then rotate the reflection image 90 clockwise about point P. b) Draw and label both images. c) What can you say about the triangle and its final image? How can you check? 3. Describe a pair of transformations that move the shape to its image. Find as many pairs of transformations as you can. 9

10 I can perform a combination of successive transformations of 2-D shapes to create a design, and identify and describe the transformations. 1. Copy this diagram on grid paper. Draw and label both images each time. a) Translate the quadrilateral 5 squares right and 1 square up. Then translate the image 2 squares left and 3 squares down. b) Rotate the quadrilateral 90 clockwise about vertex C. Then rotate the image 180 about point S. 2. Draw a quadrilateral on grid paper. a) Choose 2 successive translations, reflections, or rotations. Apply the first transformation to the quadrilateral. Then apply the second transformation to the image. b) Label the vertices of each image. c) What can you say about the quadrilateral and each of its images? How could you check? 3. Describe 2 successive transformations that move ABC to its final image, A''B''C''. 10

11 Show your work. Show What You Know Transformations and Coordinates 1. Draw and label a coordinate grid. a) Plot each point on the grid. What scale will you use? Explain your choice A(2,6) B(4,14) C(12,14) D(8,10) E(10,2) 2. Copy ΔDEF on a coordinate grid. For each transformation below: - draw the image after the transformation - write the coordinates of the vertices of the image - describe how the positions of the vertices of the triangle have changes a) translation of 4 squares left and 1 square down b) a reflection in the vertical line through the horizontal axis at 5 c) a 90 o counterclockwise rotation about vertex E 11

12 3. a) Describe as many different single transformations as you can that move the octagon to its image b) For each transformation, label the vertices of the image. 4. Draw and label both images each time. a) Translate the octagon 2 squares right and 3 squares down. The translate the image 4 squares left and 4 squares up. b) Reflect the octagon in a line through DE. Then reflect the image in the given line of reflection. 12

13 c) Rotate the octagon 90 o clockwise about point F. Then rotate the image 180 o about point J. d) What can you say about the octagon and all of its images? 5. a) Rotate the hexagon 180 o about (4,7). Then reflect the rotation image in a line through FE. Draw and label both images. b) What are the coordinates of the vertices of the final image? 6. a) Describe two successive transformations that move the shape to its image. b) Find as many pairs of transformations as you can. 13

14 7. This design was formed by repeatedly transforming 2 shapes. a) Copy the design. Identify 2 original shapes. b) Describe the transformations that could have been used to create the design. c) Is another set of transformations possible? If your answer is yes, describe the transformations. d) Use the 2 original shapes and transformations to make a different design. Describe the transformations you used. 14