1. Translations Geometry – Unit 2

2. Translations using Digital Technology  http://www.mathopenref.com/translate.html http://www.mathopenref.com/translate.html

3. Vectors  Translation occurs along a given VECTOR:  A vector is a __________________ in a plane. One of its two endpoints is known as a starting point; while the other is known simply as the __________________________.  A vector indicates both _______________________ and magnitude (____________________). The arrow on the end of the vector shows the direction of travel.  Pictorially, note the starting and endpoints: A B A B segment Ending point direction Size or length

4.  A translation of a figure along a given vector is a basic rigid motion of that figure.  Three basic properties of translation are:  A translation maps a line to a line, a ray to a ray, a segment to a segment, and an angle to an angle.  A translation preserves ___________________________ of segments.  A translation preserves ___________________________ of angles.  A translation is an __________________________________ that maps all points of a figure the same distance, and in the same direction.  “ ____________________” the length Degree measures isometry SLIDE

5. Example 1  Name the vector in the picture below.

6. Example 2:  Name the vector along which a translation of a plane would map point A to image A’. A’

7. Example 3: The distance and the direction is the same.

8. Example 4  Draw the vector that defines each translation below.

9. Vector notation

10. Example 5: Translating Using Vectors  Using the diagram to the right. Find the image of Q under the translation described by vector. Find the vector that describes the translation T  S. x-direction y-direction Q’ We move from point T to the right 6 units (x-direction) We then move up 4 units (y-direction) Now that we know the movements, we can write the vector =

11.  Using variables, you can say that the vector maps each (x, y) pair to (x + a, y + b).  The rule is: (x, y)  (x + a, y + b)

12. Example 6: Writing a rule that describes translations. Step 1: Select a point in the preimage In this case, I selected Point A Step 2: Find the change in the x-direction (horizontal change) to the corresponding image, A’. Using the graph, we can count over. (-4,1) (2,0) OR we can find the change in the x-direction by finding the difference between the x-coordinates. x 2 -x 1 **ALWAYS subtract the coordinates of your starting point from your ending point when dealing with vectors!!!

13. Example 6: Writing a rule that describes translations. Change in x = 2 – (-4) = 6 (to the right 6 units) Step 3: Find the change in the y-direction (vertical change) to the corresponding image, A’. Using the graph, we can count down. (-4,1) (2,0) OR we can find the change in the y-direction by finding the difference between the y-coordinates. y 2 -y 1 Change in y = 0 – 1 = -1 (down one unit)

14. Example 6: Writing a rule that describes translations. (-4,1) (2,0) Step 4: What is the vector, ? Step 5: Plug into the general rule, (x, y)  (x + a, y + b) (x, y)  (x + 6, y - 1)

15. “T” for translation x and y movement of the figure

16. Example 7: The “T” indicates a translation, or a “slide.” The vector indicates a slide to the left 2 units, and a slide up 7 units. Using the general rule, we can write: (x, y)  (x -2, y + 7)

17. HOMEWORK  Halloween Translation Worksheet