Thursday, September 25, 2014

Transformations Review Activity


Below is the Geogebra applet for problem 1 showing three line segments.  One of the segments is independent and the position of the other two depends on the first.  Which line segment is independent from the others?  You can drag line segments or points in the applet below.

For this diagram the blue segment maps to the orange segment (reflection about the y-axis), and the orange segment maps to the purple segment (translation right 3 and up 2).  We can also think about which points are independent/dependent, and about the mapping between the points.  Point A maps to point F, which is then mapped to point D.  The type of transformation that maps the points is the same as the transformation that maps the segments (reflection then translation).

The objectives for student use of this lesson are to identify the types of transformations for each problem (2 per problem), write the coordinate rule for each transformation, find the image of a point given the pre-image, or find the pre-image of a point given the image.  Since there are two tranformations per problem, vocabulary might get in the way of understanding.  The organizer below can facilitate conversations about the objectives, and can help students organize their thinking.  I would model the thinking and fill out this entire organizer with students before they get started with practice on their own.

Completed Organizer for problem 1:

This activity is still in the draft stage, but my plan is to have students use the exact same organizer for each problem.  I suspect that rotations might be hard for students to see, so I might model problem 2 as well so we can do the first problem with rotations together.  

There is no answer key yet, but the transformations for each problem are:

1.  Reflect about y-axis, then translate 3 units right and 2 units up. Begin with segment AB.

2.  Translate two units left and 5 units down, then rotate 90 degrees counterclockwise about origin.  Begin with segment CF.

3. Rotate 180 degrees counterclockwise about the origin, then translate 7 units left and 3 units up. Begin with segment BD.

4.  Translate 6 units left and 10 units down, then reflect about the x-axis.  Begin with segment AF.

5.  (This is supposed to be problem 6, looks like I missed an upload).  Dilate by a factor of 3 with center at origin, then translate 8 units left.  Begin with segment BF.

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