1.7 Translations

1. 1.7 Translations Warm Up Find the coordinates of the image of with vertices A(3, 4), B(5, –2), after each reflection. 1. across the x-axis 2. across the y-axis 3. across the line y = x

2. 1.7 Translations Warm Up Find the coordinates of the image of with vertices A(3, 4), B(5, –2), after each reflection. 1. across the x-axis 2. across the y-axis 3. across the line y = x

3. 1.7 Translations Objective Identify and draw translations.

4. A translation is a transformation where all the points of a figure are moved the same distance in the same direction. A translation is an isometry, so the image of a translated figure is congruent to the preimage. A C B A’ C’ B’

5. Example 1 Tell whether each transformation appears to be a translation. A. B. Yes; all of the points have moved the same distance in the same direction. No; not all of the points have moved the same distance. C. D. No; the figure appears to be flipped. Yes; the figure appears to slide.

6. To find coordinates for the image of a figure in a translation, add a to the x-coordinates of the preimage and add b to the y-coordinates of the preimage. Translations can also be described by a rule such as (x, y)  (x + a, y + b).

7. Example 2 Find the coordinates for the image of ∆ABC after the translation (x, y)  (x + 2, y - 1). Draw the image. • Example 3 • Find the coordinates for the image of JKLM after the translation • (x, y)  (x – 2, y + 4). • Draw the image.

8. Example 4 Translate the quadrilateral with vertices R(2, 5), S(0, 2), T(1,–1), and U(3, 1) after the translation (x, y) →(x – 4, y – 3). Draw the image.

9. A’ A Example 5 The figure shows part of a tile floor. Write a rule for the translation of hexagon 1 to hexagon 2.

10. A’ • Example 6 • Use the diagram to write a rule for the translation of square 1 to square 3.