Home
Published on Texas Gateway (https://texasgateway.org)
i

Website Maintenance Notice

We’re currently performing scheduled maintenance to update and improve our site. Some content may be temporarily unavailable as we retire legacy materials that no longer meet current standards. Thank you for your patience as we work to enhance your experience.
Exploring Dilations

Exploring Dilations


A dilation is a type of transformation. Other transformations include translations, reflections, and rotations.

The result of a transformation is called the image. The original figure is called the pre-image.

Use the link below to explore dilations:

  • Click on the ACTIVITIES button at the top of the screen.
  • Follow the directions for “Playing with Dilations” that appear on the right side of the screen.
  • Click on either the left or right arrow near the top right of the screen. Follow the directions for “Hitting a Target” that appear on the right side of the screen.
Playing with Dilations

After you have explored some dilations, answer the following questions in your math journal. Use the words pre-image and image in your responses.

  1. When you dragged the blue slider, how did the image compare to the pre-image? What stayed the same? What changed?
  2. When you rotated the pre-image, how did the image compare to the pre-image? What stayed the same? What changed?
  3. When you dragged the black point on the white line (the center of dilation), how did the image compare to the pre-image? What stayed the same? What changed?
  4. Use the word bank to complete the sentences below:
    1. A dilation is a transformation that changes the __________ and ____________ of a figure. A dilation does not change the figure’s _____________.
    2. The result of a dilation is called the ________. The original figure is called the __________.
    3. If the image is smaller than the pre-image, the dilation is a __________.
    4. If the image is larger than the pre-image, the dilation is a __________.

WORD BANK:

pre-image, size, enlargement, position, image, orientation, reduction

 

Dilations on a Coordinate Plane

Exploring Dilations


The result of a transformation is called the image. The original figure is called the pre-image.

Watch this video to observe the dilation of a triangle. As you watch, notice the following:

  • The center of dilation is the origin.
  • The term “k-factor” is used in the video. This is also known as a “scale factor.”

Respond to or complete the following in your math journal:

  1. How did the x coordinates of the image compare to the corresponding x coordinates of the pre-image?
  2. How did the y coordinates of the image compare to the corresponding y coordinates of the pre-image?
  3. The dilation in the video was an enlargement using a scale factor of 2 and could be represented with the rule (2x, 2y). Describe the dilation represented by the ruleCoordinate: one third x, one third y.
  4. Use the words enlargement and reduction to fill in the blanks:
    If the scale factor is between 0 and 1, the dilation will be __________________.
    If the scale factor is greater than 1, the dilation will be ______________________.