Unit 1, Lesson 18
Practicing Point-by-Point Transformations (Optional)
Geometry
18.1
Warm-up
Instructional Routines
NoneMaterials
NoneActivity Narrative
The purpose of this Warm-up is for students to understand the idea behind the “Obstacle Course” activity in this lesson. Students imagine all rigid motions are being done physically in the plane, so they are not allowed to do a translation or rotation where the physical motion would take the figure through a solid obstacle.
Launch
NoneActivity
NoneDescribe the transformations needed to get through the maze.
Student Response
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Building on Student Thinking
Activity Synthesis
Invite students to share their sequence of transformations and demonstrate the location of the figure after each transformation. If any student uses a reflection to jump over a barrier, congratulate them for thinking of this option, and inform them the barriers in the next activity are too tall to jump over.
Student Lesson Summary
Sometimes it's not hard to figure out a transformation that takes all the points of one figure directly to all the points of its image. Here, it looks like there is a 90-degree rotation that will take figure to figure . It is not obvious where the center of rotation would be though.
Instead, we could describe the transformation in two steps. First, translate figure by the directed line segment . Next, rotate the image of clockwise by angle using center . It looks like this is a 90-degree rotation, but we can be sure the rotation will work if we use the labels to define the rotation instead of an angle measure. This method of matching up one point at a time until the whole figure has been taken to the image will work for any transformation, including ones in which it's hard to see a single transformation from one figure to the other.