Lesson 5: Coordinate Moves
About this lesson
Students continue to investigate the effects of transformations. The new feature of this lesson is the coordinate plane. In this lesson, students use coordinates to describe figures and their images under transformations in the coordinate plane. Reflections over the \(x\)axis and \(y\)axis have a very nice structure captured by coordinates. When we reflect a point like \((2,5)\) over the \(x\)axis, the distance from the \(x\)axis stays the same but instead of lying 5 units above the \(x\)axis the image lies 5 units below the \(x\)axis. That means the image of \((2,5)\) when reflected over the \(x\)axis is \((2,\text5)\). Similarly, when reflected over the \(y\)axis, \((2,5)\) goes to \((\text2,5)\), the point 2 units to the left of the \(y\)axis.
Using the coordinates to help understand transformations involves MP7 (discovering the patterns coordinates obey when transformations are applied).
Lesson overview
 5.1 Warmup: Translating Coordinates (5 minutes)

5.2 Activity: Reflecting Points on the Coordinate Plane (15 minutes)
 There is a digital applet in this activity.

5.3 Activity: Transformations of a Segment (15 minutes)
 Includes "Are you Ready for More?" extension problem
 There is a digital applet in this activity.
 Lesson Synthesis
 5.4 Cooldown: Rotation or Reflection (5 minutes)
Learning goals:
 Draw and label a diagram of a line segment rotated 90 degrees clockwise or counterclockwise about a given center.
 Generalize (orally and in writing) the process to reflect any point in the coordinate plane.
 Identify (orally and in writing) coordinates that represent a transformation of one figure to another.
Learning goals (student facing):
 Let’s transform some figures and see what happens to the coordinates of points.
Learning targets (student facing):
 I can apply transformations to points on a grid if I know their coordinates.
Required materials:
 geometry toolkits
Glossary:
 coordinate plane  The coordinate plane is a system for telling where points are. For example. point \(R\) is located at \((3, 2)\) on the coordinate plane, because it is three units to the right and two units up.
 Access the complete Grade 8 glossary.
Standards:
 This lesson builds on the standard:CCSS.8.G.A.1MS.8.G.1
 This lesson builds towards the standard:CCSS.8.G.A.3MS.8.G.3
IM 6–8 Math was originally developed by Open Up Resources and authored by Illustrative Mathematics, and is copyright 20172019 by Open Up Resources. It is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0). OUR's 6–8 Math Curriculum is available at https://openupresources.org/mathcurriculum/.
Adaptations and updates to IM 6–8 Math are copyright 2019 by Illustrative Mathematics, and are licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).
Adaptations to add additional English language learner supports are copyright 2019 by Open Up Resources, and are licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).
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