1. 9-2: Translations

2. Translation-
A transformation that moves all points of a figure the same distance in the same direction.
A slide
an isometry.
Up or down – changes y coordinate
Left or right – changes x coordinate

3. Ways to write translations:
Words
EX: Translate up 3 units and to the left 4 units.
Coordinates
EX: (x,y)→(x-4,y+3)
Matricies
EX:

4. Examples: Translate the point (4,-3) to the left four units.
Translate the triangle ABC with A(-2,4), B(6,5) and C (0,0) down 7 units and to the right 10 units.
Given the following vertex matrix for quadrilateral ABCD,
translate the shape to the left 13 units.

5. More Examples
4. Quadrilateral ABCD is translated up 3 units and to the left one unit. If the coordinates of A’B’C’D’ are A’(3,4), B’(0,0), C’(0,5), and D’ (-3,2), what are the coordinates of the preimage?

6. Translation or Reflection?

7. Composition of reflection:
Reflecting an image over a line, and then reflecting it again over a line parallel to the first line of reflection.
Composition of reflections always results in a translation.

8. Is this a composition of reflections?

9. Putting it all together: Composition of transformations
Composition of transformations- doing two or more transformations to an object.
ORDER MATTERS.

10. Given A(3,4), B(2,5) and C(9,-5) Write the vertex matrix.
Reflect over the x-axis.
Translate up 5 units.
Reflect over the line y=x
Translate to the left 6 units.

11. Practice:
Do WB 9-2

12. Answers: No; it is a translation of a reflection.
Yes, it is a reflection of a reflection with respect to parallel lines. 3. 4.
5. (x+4,y+2) 6. (x-4, y+1) 7. (x+3, y+3)