In this section, you will use an interactive sketch to investigate translations. Click on the following link to open the applet in a new tab/window.

Transmographer

This sketch allows you to investigate the changes in coordinates when a translation is applied to a geometric figure.

Translations

First, let’s investigate translations.

1. Use your notes to record the initial coordinates of the green point, yellow point, cyan point, and black point.
2. In the Translate box, type 3 units on the x-axis and 2 units on the y-axis.
3. Click the Translate button.
4. Record the new coordinates of each point.
5. How did the value of the coordinates change?
   Interactive popup. Assistance may be required.

   Check Your Answer

   The x coordinates all increased by 3 and the y coordinates all increased by 2.
6. How was the size and shape of the figure affected?
   Interactive popup. Assistance may be required.

   Check Your Answer

   The size and shape did not change.
7. Repeat this process using different polygons and different translation values.
8. In general, how are the x and y-coordinates affected when a translation is applied to the figure?
   Interactive popup. Assistance may be required.

   Check Your Answer

   The x coordinates all increased or decreased by the change in the x value and the y coordinates all increased or decreased by the change in the y value.

We can write the rule for translations in symbolic language.

Translation (x, y) → (x + a, y + b)

In general, how are the size and shape of a figure affected when a translation is applied to the figure?

Interactive popup. Assistance may be required.

Check Your Answer

The size and shape did not change.

Since the size and shape of figures are not affected by translations, we say translations are congruence transformations.