Unit 1, Lesson 18
Practicing Point-by-Point Transformations
Integrated Math 1
18.1
Warm-up
Describe the transformations needed to get through the maze.
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Describe the transformations needed to get through the maze.
For each diagram, find a sequence of translations and rotations that take the original figure to the image so that if done physically, the figure would not touch any of the solid obstacles and would not leave the diagram. Test your sequence by drawing the image of each step.
Take to .
Take to .
For each question, describe a sequence of translations, rotations, and reflections that will take parallelogram to parallelogram .
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.