1. Translation (slide) TRANSLATION a slide without turning.
If you have a given repeating pattern, you can slide it along a certain direction a certain distance and it will fall back upon itself with all the patterns exactly matching. This symmetry is called a translation.
TRANSLATION: Translate means to slide. A translation moves a figure a given distance in a given direction. You can think of a translation as sliding an image across a piece of paper.
specified by a direction and a distance.

2. Transformations Image (transformed figure)
Changes position or orientation of a figure.
(preserves size & shape but changes location)
Each point of original figure is paired with exactly one point of its image on the plane.
Image (transformed figure)
(congruent to original figure.)
We can identify a symmetry as a transformation of the plane that moves the pattern so that it falls back on itself. The only transformations that we'll consider are those that preserve distance, called isometries. (Self-similar fractals have symmetries on different scales, and so other transformations must be considered to understand them.) There are four kinds of planar isometries: translations, rotations, reflections, and glide reflections
indicated with “prime” notation

3. Translation (SLIDE) ‘Prime notation’
Each point of R is “moved” to a new position R’
R’ is the image of R.
‘Prime notation’
image
Translation (SLIDE) l
Move without rotating or reflecting
Every translation has a direction and a distance
moves a figure
over,
down,
or up.

5. Use‘Transformation notation’ to move an image.
(x,y)→(x+3, y)
(x,y)
(x,y)
(-6,-2)→(-6+3, -2)→(-3, -2)
(x,y)
(-6,-5)→(-6+3, -5)→(-3, -5)
(x,y)
(-4,-5)→(-4+3, -5)→(-1, -5)

9. Can you do same transformation twice?
Or combine more than 2 transformations?
(x,y)→(x+5, y)

10. You Try (Create the new image by translating them.
(x,y)→(x+5, y)
(x,y)→(x-1, y + 4)

11. (x,y)→(x+5, y) (-6,-2)→(-6+5, -2)→(-1, -2) (x,y) (x,y)
(-6,-5)→(-6+5, -5)→(-1, -5)
(x,y)
(-4,-5)→(-4+5, -5)→ (1, -5)
(x,y) l

12. (x,y)→(x-1, y + 4)
(-6,-2)→(-6-1, )→(-7, 2)
(x,y)
(x,y)
(-6,-5)→(-6-1, )→(-7, -1)
(x,y)
(-4,-5)→(- 4-1, )→ (-5, -1)
(x,y)

13. Left 3 and up 1 Down 5 (-3, 5), (-4, 0), (0, -3), (1, 2)
TRY THESE
1. Explain how a figure is translated for (-3, 1).
Explain how a figure is translated for (0, -5).
Reflect over the y-axis: (3, 5), (4, 0), (0, -3), (-1, 2).
Reflect over the x-axis: (-5, 2), (3, 0), (-1, -2).
Left 3 and up 1
Down 5
(-3, 5), (-4, 0), (0, -3), (1, 2)
(-5, -2), (3, 0), (-1, 2)

14. 1. The image of point (3,-5) under the translation that shifts (x,y) to (x-1,y-3) is.....
A. (-4,8) B. (2,8) C. (-3,15) D. (2,-8)
image of point (3,-5) under translation that shifts (x,y) to (x-1,y-3) is (2,-8)
2. A translation maps (x,y) (x+1,y+2) what are
the coordinates of B (-2,4) after translation?
coordinates of B(-2,4) after translation: (-1,6).
3. What is the image of point P(-3,2) under the transformation T(2,6)?
T(-2,6) means add -2 to the x-value (-3) & +6 to the y-value (2). image of point P is (-5,8).

15. What is the image of point P(4,2) under the transformation T(-2,2)?
The image of point P(4,2) under the transformation T(-2,2) is (2,4).
What is the image of point P(-2,-7) under the transformation T(6,4)?
The image of point P(-2,-7) under the transformation T(6,4) is (4,-3).
If the point (4,1) has a translation of (-2,4), what are the coordinates of pt. (-1,5) under the same translation?
To solve this problem, you have to add (-2,4) to the point (-1,5). Always add x-value with x-value and vice-versa (For example: add -2 to -1 and add 4 to 5.) The answer is (-3,9).

16. If the coordinates of the vertices of triangle ABC are A(-4,-1), B(-1,5) and C(2,1), what are the coordinates of triangle A'B'C', the translation of triangle ABC, under T(4,3)?
The coordinates of triangle A‘ B‘ C' are A'(0,2), B'(3,8) and C'(6,4).
How do we translate points & figures in a coordinate plane?