1. 9.1 – Translate Figures and Use Vectors

2. Transformation:
Moves or changes a figure
Preimage:
Original figure
Image:
Transformed figure
“P prime”
Isometry:
A congruent transformation

3. Translation:
An isometry that moves every point a certain distance in a certain direction P Q

4. Translation:
Note:
and

5. Motion Rule:
Moves each point left, right, down, or up
Down or Up
Left or
Right

6. Use the translation
What is the image of D(4, 7)?
(4 + 2, 7 – 5) D +2
(6, 2) –5

7. Use the translation
What is the image of R(2, –4)?
(2 – 7, –4 + 4)
(–5, 0) +4 –7 R

8. Use the translation
What is the preimage of (–5, 3)? M
(–5 – 4, 3 + 6)
(–9, 9) +6 –4

9. Use the translation
What is the preimage of (4, –1)?
(4 + 5, –1)
(9, –1) +5 A

10. (–1 – 3, 1 + 5) (–4, 6) C (4 – 3, –1 + 5) A (1, 4) B (2 – 3, 4 + 5)
The vertices of ABC are A(–1, 1), B(4, –1), and C(2, 4). Graph the image of the triangle using prime notation.
(–1 – 3, 1 + 5)
(–4, 6) C
(4 – 3, –1 + 5) A
(1, 4) B
(2 – 3, 4 + 5)
(–1, 9)

11. (–1 , 1 – 3) (–1, –2) C (4, –1 – 3) A (4, –4) B (2, 4 – 3) (2, 1)
The vertices of ABC are A(–1, 1), B(4, –1), and C(2, 4). Graph the image of the triangle using prime notation.
(–1 , 1 – 3)
(–1, –2) C
(4, –1 – 3) A
(4, –4) B
(2, 4 – 3)
(2, 1)

12.  is the image of ABC after a translation
 is the image of ABC after a translation. Write a rule for the translation. +3 –5

13.  is the image of ABC after a translation
 is the image of ABC after a translation. Write a rule for the translation. +2 –5

14. Vector:
Translates a shape in direction and magnitude, or size.
Written: FG
Where F is the initial point and G is the terminal point.

15. Vector:
Component form:
< x, y >

16. Name the vector and write its component form.JD +5 –1

17. Name the vector and write its component form.DR –7 –3

18. Name the vector and write its component form.RS –4

19. Use the point P(5, –2). Find the component form of the vector that describes the translation to+2 –3 P

20. Use the point P(5, –2). Find the component form of the vector that describes the translation to
–10 –2 P

21. Find the value of each variable in the translation.
80°
2b = 8
b = 4
c = 13
5d = 100
d = 20°

22. Find the value of each variable in the translation.
180 – 90 – 31
a = 59°

23. 9.3 – Perform Reflections

24. Reflection:
Transformation that uses a line like a mirror to reflect an image
Line of Reflection:
Mirror line in a reflection

25. A reflection in a line m maps every point P in the plane to a point , such that:
If P is not on m, then m is the perpendicular bisector of
If P is on m, then

26. Reflect point P(5, 7) in the given line.
x – axis
P(5, 7) becomes P
A reflection in the x-axis changes
(x, y) into _______
(x, –y)

27. Reflect point P(5, 7) in the given line.
y – axis
P(5, 7) becomes P
A reflection in the y-axis changes
(x, y) into _______
(–x, y)

28. Reflect point P(5, 7) in the given line.
y = x
P(5, 7) becomes P
A reflection in the y = x changes
(x, y) into _______
(y, x)

29. Graph the reflection of the polygon in the given line.
x – axis

30. Graph the reflection of the polygon in the given line.
y – axis

31. y = x (–1 , –3) (–3, –1) (2, –4 ) (–4, 2) (3, 0) (0, 3)
Graph the reflection of the polygon in the given line.
y = x
(–1 , –3)
(–3, –1)
(2, –4 )
(–4, 2)
(3, 0)
(0, 3)

32. Graph the reflection of the polygon in the given line.
x – axis

33. Graph the reflection of the polygon in the given line.
x = –1

34. Graph the reflection of the polygon in the given line.