Illustrative Mathematics Grade 8, Unit 1, Lesson 5: Coordinate Moves

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Illustrative Math
Grade 7

Lesson 5: Coordinate Moves

Let’s transform some figures and see what happens to the coordinates of points.

Illustrative Math Unit 8.1, Lesson 5 (printable worksheets)

Lesson 5 Summary

The following diagram shows how to use coordinates to describe points and find patterns in the coordinates of transformed points for translations, rotations, and reflections.

Lesson 5.1 Translating Coordinates

Select all of the translations that take Triangle T to Triangle U. There may be more than one correct answer.

1. Translate (-3,0) to (1,2).
2. Translate (2,1) to (-2,-1).
3. Translate (-4,-3) to (0,-1).
4. Translate (1,2) to (2,1).

• See Video for Whole Lesson

Lesson 5.2 Reflecting Points on the Coordinate Plane

1. Five points are plotted on the coordinate plane.
   Open Applet
   a. Using the Pen tool or the Text tool, label each with its coordinates.
   b. Using the x-axis as the line of reflection, plot the image of each point.
   c. Label the image of each point using a letter. For example, the image of point should be labeled A'.
   d. Label each with its coordinates.
2. If the point (13,10) were reflected using the x-axis as the line of reflection, what would be coordinates of the image? What about (13,-20)? (13,570)? Explain how you know.
3. The point R has coordinates (3,2).
   a. Without graphing, predict the coordinates of the image of point R if point R were reflected using the y-axis as the line of reflection.
   b. Check your answer by finding the image of R on the graph.
   c. Label the image of point R as R'.
   d. What are the coordinates of R'?
4. Suppose you reflect a point using the -axis as line of reflection. How would you describe its image?

Lesson 5.3 Transformations of a Segment

The applet has instructions for the first 3 questions built into it. Move the slider marked “question” when you are ready to answer the next one. Pause before using the applet to show the transformation described in each question to predict where the new coordinates will be.
Apply each of the following transformations to segment AB. Use the Pen tool to record the coordinates.

1. Rotate segment AB 90 degrees counterclockwise around center B by moving the slider marked 0 degrees. The image of A is named C. What are the coordinates of C?
2. Rotate segment AB 90 degrees counterclockwise around center A by moving the slider marked 0 degrees. The image of B is named D. What are the coordinates of D?
3. Rotate segment AB 90 degrees clockwise around (0,0) by moving the slider marked 0 degrees. The image of A is named E and the image of B is named F. What are the coordinates of B and F?
4. Compare the two 90-degree counterclockwise rotations of segment AB. What is the same about the images of these rotations? What is different?
   Open Applet
   

Are you ready for more?

Suppose EF and GH are line segments of the same length. Describe a sequence of transformations that moves EF to GH.

Lesson 5 Practice Problems

1. a. Here are some points.
   What are the coordinates of A, B, and C after a translation to the right by 4 units and up 1 unit? Plot these points on the grid, and label them A', B' and C'.
   b. Here are some points.
   What are the coordinates of D, E, and F after a reflection over the y-axis? Plot these points on the grid, and label them D', E' and F'.
   c. Here are some points.
   What are the coordinates of G, H, and I after a rotation about (0,0) by 90 degrees clockwise? Plot these points on the grid, and label them G', H' and I'.
2. Describe a sequence of transformations that takes trapezoid A to trapezoid B.
3. Reflect polygon P using line l.

The Open Up Resources math curriculum is free to download from the Open Up Resources website and is also available from Illustrative Mathematics.

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