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

When you dragged the arrow head, how did the image compare to the pre-image? What stayed the same? What changed?

When you dragged the pre-image, how did the image compare to the pre-image? What stayed the same? What changed?

How did dragging the pre-image compare to dragging the arrow head? How were these translations alike? How were they different?

When you dragged a vertex of the pre-image, how did the image compare to the pre-image? What stayed the same? What changed?

Use the word bank to complete the sentences below:

A translation is a transformation the changes the ________________ of a figure. A translation does not change the figure’s _________ or ________________.

The result of a translation is called the ________. The ____________ figure is called the pre-image.

For any translation, the image and pre-image are ______________.

WORD BANK:

Image, size, congruent, orientation, original, position

Translations on a Coordinate Plane

Translations on a Coordinate Plane

Record the coordinates of the vertices of a translated polygon as follows:

Use a capital letter for each vertex of the pre-image. For example, a triangle could have vertices at points A, B, and C.

Use corresponding capital letters to identify corresponding vertices of the image, adding a prime symbol (‘). For example, the image of the triangle with vertices A, B, and C would have vertices A’, B’, and C’.

The vertices of the image are read as follows: “A prime,” “B prime,” and “C prime.”

Watch this video to observe the translation of a right triangle.

Respond to or complete the following in your math journal:

Summarize the two methods used in the video for translating the triangle.

How did the x coordinates of the image compare to the corresponding x coordinates of the pre-image?

How did the y-coordinates of the image compare to the corresponding y coordinates of the pre-image?

The translation in the video of 9 units to the right and 4 units down could be represented using the rule (x + 9, y – 4). Describe the translation represented by the rule (x – 2, y + 3).

Generating Translations

Generating Translations

Use the link below to explore translations of irregular polygons:

Click on the ACTIVITIES button at the top of the screen.

Follow the directions for “Playing with Translations” that appear on the right side of the screen.

Check the box near the bottom left to turn the axes on.

Drag the pre-image and/or the arrow head to illustrate translations represented by each of the following rules:

(x + 5, y – 5)

(x – 2, y + 7)

(x – 4, y – 6)

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.

Check the box near the bottom left to turn the axes on

Determine the approximate rule that could be used to describe this translation: (_________, _________)