Integrated Math 2 – WS 7-1 – Translating Graphs
Name _______________________________
1. What does it mean to translate a shape?
For the following worksheet you will need two colored pencils/markers/crayons, one blue and the other red. First
color the shape in each coordinate plane blue. This will be considered your original image, or preimage. Next you
will perform the translation directed in each coordinate plane. Please color your new image red.
Translate: Right 5 and Up 5
A’ _______
B’ ________
C’ __________
Translate: Down 3 and Right 6
A’ _______
B’ ________
C’ __________
Translate: Left 3 and Up 5
A’ _______
B’ ________
C’ __________
Translate: Down 4 and Left 3
A’ _______
B’ ________
C’ __________
2. By looking at the slope of each line (you do not need to find the slope), do you think the slope changes when you
translate an object? Why or why not?
Translate: Right 6 and Down 3
Translate: Left 3 and Up 7
A’ _________
B’
_________
A’ _________
B’
_________
C’ _________
D’
_________
C’ _________
D’
_________
Translate: Up 5 and Right 5
Translate: Down 5 and Left 2
A’ _________
B’
_________
A’ _________
B’
_________
C’ _________
D’
_________
C’ _________
D’
_________
3. By looking at the length of each line (you do not need to find the distance), do you think the distance changes
when you translate an object? Why or why not?
Integrated Math 2 – WS 7-2 – Translating Ordered Pairs
Name _______________________________
Use the coordinates A(-4, 2) and B(8, -1) as the preimage for problems 1-5.
1. Find the slope of AB
Find the new coordinates after each translation below. Then find the slope of the new line.
2. right 16
3. Down 14
4. up 28 and right 13
5. Down 31 and left 5
Use the coordinates C(-2, 9) and D(3,4) as the preimage for problems 6-10.
6. Find the distance of CD
Find the new coordinates after each translation below. Then find the distance of the new line.
7. up 17
8. Left 23
9. Right 16 and down 25
10. Up 14 and left 19
11. Explain using complete sentences why slope and distance will never change when translating an object.
Integrated Math 2 – WS 7-3 – Reflecting Graphs
Name _______________________________
1. What does it mean to reflect a shape?
For the following worksheet you will need two colored pencils/markers/crayons, one blue and the other red. First
color the shape in each coordinate plane blue. This will be considered your original image, or preimage. Next you
will perform the reflection directed in each coordinate plane. Please color your new image red. Then answer the
questions that follow.
2. Reflect over the y-axis
3. Find the new coordinates.
A’ ______
B’ ______
C’ ______
D’ ______
4. Find the slope of AB
5. Find the slope of A’B’
6. Did the slope change? Explain.
7. Find the distance of CD
8. Find the distance of C’D’
9. Did the distance change? Explain.
10. Reflect over x-axis
11. Find the new coordinates.
A’ ______
B’ ______
C’ ______
12. Find the slope of AB
13. Find the slope of A’B’
14. Did the slope change? Explain.
15. Find the distance of CD
16. Find the distance of C’D’
17. Did the distance change? Explain.
D’ ______
18. Reflect over the y-axis
19. Find the new coordinates.
A’ ______
B’ ______
C’ ______
D’ ______
20. Find the slope of AB
21. Find the slope of A’B’
22. Did the slope change? Explain.
23. Find the distance of CD
24. Find the distance of C’D’
25. Did the distance change? Explain.
26. translate 2 units right and three units down, then reflect over the x-axis
27. Find the new coordinates.
A’ ______
B’ ______
C’ ______
28. Find the slope of AB
29. Find the slope of A’B’
30. Did the slope change? Explain.
31. Find the distance of CD
32. Find the distance of C’D’
33. Did the distance change? Explain.
Answer using complete sentences.
34. What happens to the coordinates (x, y) when reflecting over the x axis?
35. What happens to the coordinates (x, y) when reflecting over the y-axis?
D’ ______
Integrated Math 2 – WS 7-4 – Reflecting Ordered Pairs
Name _______________________________
Use the coordinates A(-4, 5) and B(8, -3) as the preimage for problems 1-5.
1. Find the slope of AB
Find the new coordinates after each transformation below. Then find the slope of the new line.
2. reflect over the x-axis
3. Reflect over the y-axis
4. Up 3, left 2, reflect over x-axis
Use the coordinates C(-2, 2) and D(1, -4) as the preimage for problems 6-10.
5. Find the distance of CD
Find the new coordinates after each translation below. Then find the distance of the new line.
6. reflect over the y-axis
7. Reflect over the x-axis
8. Right 5, down 2, reflect over y-axis
Answer the following questions using complete sentences.
9. Does the slope change when reflecting a line? If not, why? If so, how?
10. Does the distance change when reflecting a line? If not, why? If so, how?
7-5 Alice in Wonderland
Delicious Dilations
Activity adapted from The Mathematics of Alice’s Adventures in Wonderland by Susan B. Taber.
In the story, Alice’s Adventures in Wonderland, Alice changes size 12 times during her
adventures. The changes occur when she drinks a potion or eats a cake. Problems occur throughout her
adventures because Alice does not know when she will grow larger or smaller. Eventually, Alice
controls her size changes by nibbling sides of a
mushroom. This allows Alice to control her size and use her height
changes to her advantage when necessary. Find the changes in Alice’s height after she drinks each
potion or eats each bite of cake. Then write an equation to represent the change.
Starting Height
Potion or Cake
New Height
Equation
54 inches
1/3 as tall
18 inches
54 x 1/3 = 18
54 inches
2 times as tall
36 inches
¼ times as tall
36 inches
5 times
60 inches
2/3 times as tall
60 inches
3 times as tall
18 inches
1/6 times as tall
18 inches
4 times as tall
1. Describe the mathematical situation when Alice gets bigger?
2. Describe the mathematical situation when Alice gets smaller?
*The number that Alice grows or shrinks by is called the SCALE FACTOR. The scale
factor determines how much bigger (or smaller) a dilated object will become.
3. Graph, label, and connect the following points in order.
A (-2, 3)
D (4, -1)
G (-4, -1)
B (2, 3)
E (4, -3)
H (-2, -1)
C (2, -1)
F (-4, -3)
Connect point H to point A.
4. Dilate the picture above, using the scale factor 3 (HINT: take the coordinates and multiply
all of them by 3 to get the new coordinates!) Using the same coordinate plane,
graph, label, and connect the new ordered pairs in order.
5.
6.
7.
8.
How is the image different from the pre-image? Use side lengths and slopes.
How is the image the same as the pre-image? Use side lengths and slopes.
Find the approximate area of the pre-image. Describe your method for finding area.
Find the approximate area of the new image. Describe your method for finding area.
Integrated Math 3 – WS 7- 6 – Characteristics of Rotations
Name ____________________________
1.
2.
a) Find the slope of AB and A’B’
a) Find the slope of AD and A’D’
b) How do they compare?
b) How do they compare?
c) Find the distance of AB and A’B’
c) Find the distance of AD and A’D’
d) How do they compare?
d) How do they compare?
e) How did the preimage change to end up
e) How did the preimage change to end up
in the position of the image?
in the position of the image?
Integrated Math 3 – WS 7-7 – Introducing Rotations
Name _________________________________
Determine the rotation, both degrees and direction, for each if the preimage is on the left and the image is on the
right.
10. When you rotate an object, would you think that the distance changes? Why?
11. When you rotate an object, would you think that the slope changes? Why?
Integrated Math 3 – WS 7-7 – Introducing Rotations
Name _________________________________
Determine the rotation, both degrees and direction, for each if the preimage is on the left and the image is on the
right.
10. When you rotate an object, would you think that the distance changes? Why?
11. When you rotate an object, would you think that the slope changes? Why?
Integrated Math 3 – WS 7-8 – Rotation Coordinates
Name ____________________________
1. What kind of lines form 90° angles?
2. What do you know about the slopes of lines that form 90° angles?
3.
Rotate 90o Counter-clockwise
4.
Rotate 90o Clockwise
A _____ , B _____ , C _____ , D _____
A _____ , B _____ , C _____ , D _____
A’_____ , B’_____ , C’_____ , D’_____
A’_____ , B’_____ , C’_____ , D’_____
5. Describe what happens to the coordinates when being rotated 90° clockwise.
6. Describe what happens to the coordinates when being rotated 90° counterclockwise.
7.
Rotate 90o Clockwise
8.
Rotate 90o Counter-clockwise
A _____ , B _____ , C _____ , D _____
A _____ , B _____ , C _____ , D _____
A’_____ , B’_____ , C’_____ , D’_____
A’_____ , B’_____ , C’_____ , D’_____
Integrated Math 3 – WS 7-9 – Rotation Coordinates Day 2
1.
Rotate 180o Counter-clockwise
2.
Name ____________________________
Rotate 180o Clockwise
A _____ , B _____ , C _____ , D _____
A _____ , B _____ , C _____ , D _____
A’_____ , B’_____ , C’_____ , D’_____
A’_____ , B’_____ , C’_____ , D’_____
3. What do you notice about the placement of the image in #1 and #2.
4. What happens to the coordinates when you rotate something 180°?
5.
Rotate 270o Clockwise
6. Rotate 270o Counter-clockwise
A _____ , B _____ , C _____ , D _____
A _____ , B _____ , C _____ , D _____
A’_____ , B’_____ , C’_____ , D’_____
A’_____ , B’_____ , C’_____ , D’_____
7. Rotating something 270° clockwise is the same as rotating something what other degree and direction?
8. Rotating something 270° counter-clockwise is the same as rotating something what other degree and direction?