9.2 Translations

When you ride the elevator from the lobby of the Empire State Building to the very top, are being

reflected, rotated, or translated up the building? Justify your answer.

Characteristics of a Translation:

o A translation is a transformation in which all the points of a figure are moved the same

__________________ in the same ________________.

o The translation vector is the same length as the segments joining a point and its image. In other

words, the _______________ between each image point and its pre-image point are ________.

o A vector has both _________________ and _______________________. Think about the wind

vectors on a weather map! Let’s look at how windy it is today:

http://www.wunderground.com/maps/us/WindSpeed.html

o ,AA BB , and CC have the same length as v and are ______________ to v .

Vector: __________________________________

Magnitude: _______________________________

1) The pool of a health club undergoing renovation is being moved from the center of the bottom

floor to the far right roof deck. They want to move the pool up 8 stories and to the right 6 yards.

Which of the following represents the job the construction workers need to do?

a) 8 units in the -x direction and 6 units in the +y direction

b) 6 units in the -x direction and 8 units in the +y direction

c) 6 units in the +x direction and 8 units in the +y direction

d) 8 units in the +x direction and 6 units in the +y direction

Think-About-It: Instead of writing this out in words, how could we write this transformation using

arrow notation? Using vector notation?

2. Use the grid or patty paper to translate the following figures. Label the image.

3. Determine the translation coordinate rule from the vector.

a) T (x,y) ----> (_______,________) b) T (x,y) ----> (_______,________) c) T (x,y) ----> (_______,________)

4. Determine the translation rule from the pre-image and image.

a) A (3,5) A’ (-1,3) T (x,y) ------------- > (___________ , ___________)

b) A (-4,11) A’ (3,0) T (x,y) ------------- > (___________ , ___________)

c) A (0,-8) A’ (-1,-3) T (x,y) ------------- > (___________ , ___________)

5. Given a translation rule, determine the missing point.

a) T (x,y) ------- > (x + 3, y – 5) A (-4,7) A’ (_______ , ______)

b) T (x,y) ------- > (x -7, y – 1) A (9,1) A’ (_______ , ______)

c) T (x,y) ------- > (x + 1, y + 6) A (_______ , ______) A’ (4,-1)

d) T (x,y) ------- > (x, y + 4) A (8,-4) A’ (_______ , ______)

e) T (x,y) ------- > (x + 3, y + 1) A (_______ , ______) A’ (-4,1)

f) T (x,y) ------- > (x - 8, y - 5) A (_______ , ______) A’ (-3,-3)

6. Convert between vector component form and coordinate form.

a) 5,2 ( )T A T (x,y) ------- > (______________ , ______________)

b) 0, 12 ( )T A T (x,y) ------- > (______________ , ______________)

c) 1.5, 7 ( )T A T (x,y) ------- > (______________ , ______________)

7. Write the coordinate rule that matches the description.

a) 4 down and 3 right T (x,y) ------- > (______________ , ______________)

b) left 7 and down 2 T (x,y) ------- > (______________ , ______________)

c) right 1 T (x,y) ------- > (______________ , ______________)

8. What is the resultant translation of Point A after mapping T (x,y) followed by R (x,y).

a) A (-4,8) T (x,y) ------- > (x + 3, y – 7) A’ (_____ , _____) R (x,y) ------- > (x – 8, y – 2) A’’ (_____ , _____)

b) A (2,0) T (x,y) ------- > (x - 1, y) A’ (_____ , _____) R (x,y) ------- > (x - 3, y + 3) A’’ (_____ , _____)

c) A (5,-11) T (x,y) ------- > (x +7, y - 11) A’ (_____ , _____) R (x,y) ------- > (x - 9, y + 9) A’’ (_____ , _____)

9. Can you find a shortcut to doing two translations?

10. What is the pre-image of A’(-5,4) mapped by translation T (x,y) ------ > (x – 5, y + 11)?

Directions: Given the figure or scenario, determine the translation vector that would translate the pre-

image to the image.

11) Vector = ___________________ 12) Leigh and Derek are tossing a flying disk.

Leigh stands at (2, 5) and throws the disc to

Derek at (11, 0). Find the translation vector

from Leigh to Derek.

13) A car starts from an office building, which is 5 mi east & 2 mi south of the town center. The car

travels 6 mi north, makes a left turn and then travels 8 mi.

a) What is the car’s final position?

b) What single translation vector moves the car from its starting position to its final position?

14) A community wants to move a skateboard park for safety and noise reasons. The volunteers decide

to move the skateboard park 128 feet east and 52 feet south. Assuming the positive y-axis on a

coordinate plane as north, which function (arrow notation) represents the translation coordinates of

the skate park?

a) (x, y) (x + 52, y + 128)

b) (x, y) (x + 128, y – 52)

c) (x, y) (x – 128, y – 52)

d) (x, y) (x + 128, y + 52)

15) In football, the offensive line is required to stand on the line of scrimmage. If the entire offensive

line ends up 5 yards forward, describe two possible translations that could get them to this point.

A

A’

B

B’

C

C’