Grade 8 Project #2: Transformations

PART 1: Creating an image and performing transformations

  1. You will create and draw an image that uses a minimum of 8 points and it all within one quadrant. The image can be any shape you like.
  2. You will perform 4 transformations on your image – a reflection, a translation, a dilation and a rotation. It doesn’t matter what order you do these transformations in. The transformations may all be from the original image or from the resulting images.
  3. The final result must have an image in each of the four quadrants.
  4. You should use a different color for each of the images.
  5. Write out the details of how you carried out your transformations in the order in which you did them.
  6. Which transformation type did you find the most difficult and which was the easiest? Give your reasons for your choices.

PART 2: Labeling and writing directions

  1. Label each vertex of your original image using letters such as A, B, C……
  2. Label each vertex of your transformed images using letters such as A’, B’, C’…….
  3. Write the coordinates for each of the points in all of the images on a new page.

PART 3: Recreating a drawing from written instructions

Your teacher will now pair you up with another student and you will recreate their drawing using the coordinates and directions they wrote in Part 2.

PART 4: Comparing and discussing

You will now analyze how successful you and your partner were in recreating the images

  1. Compare your original image with the image that your partner created based on your directions. Are both images the same? If not, explain in detail what mistakes were made.
  2. Repeat this procedure for each of the 4 transformations.

PART 5: Which transformation was that?

  1. You will now create a new image following the instructions in Part 1 and carry out 1 transformation of your choice on this image.
  2. Write the coordinates for the original image and the transformed image and swap these with your partner.
  3. Using these coordinates you are to identify, with clear reasons, what type of transformation took place.
  4. Create another new image and carry out 3 transformations on this image.
  5. Write down the coordinates for the original and final image only and swap these with your partner.
  6. Using these coordinates you are to identify what the three transformations were – explaining your reasoning.

Skills

  • Tell what transformation has been acted upon an image and provide a clear rationale.
  • Translate an image given its coordinates.
  • Reflect an image over a given line or axis.
  • Reflect an image 90 degrees clockwise and counter clockwise and 180 degrees clockwise and counter clockwise.
  • Explain why the figure appears the same when rotated 180 degrees clockwise or counter clockwise.
  • Dilate an image by a whole number or a fraction.
  • Know what characteristics are preserved and changed under each transformation.

Standards

  • 8G.7 Describe and identify transformations in the plane, using proper function notation (rotations, reflections, translations, and dilations.)
  • 8.G.8 Draw the image of a figure under rotations of 90 and 180 degrees
  • 8.G.9 Draw the image of a figure under a reflection over a given line
  • 8.G.10 Draw the image of a figure under a translation
  • 8.G.11 Draw the image of a figure under a dilation
  • 8.G.12 Identify the properties preserved and not preserved under a reflection, rotation, translation, and dilation

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