Geometry â Vectors and Translations
Geometry – Vectors and Translations (A)
Name: _______________________
Hour: ______
1. Name the vector and write its component form. B
M
2.
Liam is playing a battleship game against Maddie. The board shown below is Maddie’s board. Liam takes his first shot with a location of H3, which is a miss. a. If Liam moves his next shot to the right 4 and up 1 from his initial shot, will it be a hit or a miss? b. If Liam moves his next shot 〈3, −2〉 from his initial shot, will it be a hit or a miss? c. If Liam moves his next shot (𝑥, 𝑦) → (𝑥 − 1, 𝑦 + 5) from his initial shot, will it be a hit or a miss? d. Describe the how Liam needs to change his next shot from his initial shot to hit the location C8 in the following forms: Describe in Words Component Form Write a Rule
3. Point 𝐴(3,8) is translated to Point 𝐴′(5,1). Graph the two points and write a rule for the translation.
4. Point 𝐷′ (3, −1) was translated using the rule (𝑥, 𝑦) → (𝑥 − 3, 𝑦). What are the coordinates of the preimage?
5. Complete the table of the translation in all 4 representations: Show on a Graph Describe in Words
W
S
Write a Rule
U
∆𝑊𝑆𝑈 is translated 7 units to the right and 4 units down.
Component Form
6. Draw line segment ̅̅̅̅ 𝐴𝐵 with points 𝐴(2,5) and 𝐵(1,0). If ̅̅̅̅ to ̅̅̅̅̅̅ you translate 𝐴𝐵 𝐴′𝐵′ using the component form 〈−2,3〉, where will point 𝐴′ and point 𝐵′ be on the coordinate plane?
7. If you were to draw in the two vectors that translate 𝐴 to 𝐴’ and 𝐵 to 𝐵’, what shape would you create? Justify your answer.
Geometry – Vectors and Translations (B)
Name: _______________________
Hour: ______
1. Name the vector and write its component form. T
P
2.
Liam is playing a battleship game against Maddie. The board shown below is Maddie’s board. Liam takes his first shot with a location of H4, which is a miss. a. If Liam moves his next shot to the right 4 and up 1 from his initial shot, will it be a hit or a miss? b. If Liam moves his next shot 〈3, −2〉 from his initial shot, will it be a hit or a miss? c. If Liam moves his next shot (𝑥, 𝑦) → (𝑥 − 1, 𝑦 + 5) from his initial shot, will it be a hit or a miss? d. Describe the how Liam needs to change his next shot from his initial shot to hit the location C8 in the following forms: Describe in Words Component Form Write a Rule
3. Point 𝐴(2,6) is translated to Point 𝐴′(5,1). Graph the two points and write a rule for the translation.
4. Point 𝐷′ (6, −1) was translated using the rule (𝑥, 𝑦) → (𝑥 − 3, 𝑦). What are the coordinates of the preimage?
5. Complete the table of the translation in all 4 representations: Show on a Graph Describe in Words
W
S
Write a Rule
U
Component Form 〈−2, −5〉
6. Draw line segment ̅̅̅̅ 𝐴𝐵 with points 𝐴(2,5) and 𝐵(1,0). If ̅̅̅̅ to ̅̅̅̅̅̅ you translate 𝐴𝐵 𝐴′𝐵′ using the component form 〈6,3〉, where will point 𝐴′ and point 𝐵′ be on the coordinate plane?
7. If you were to draw in the two vectors that translate 𝐴 to 𝐴’ and 𝐵 to 𝐵’, what shape would you create? Justify your answer.
Geometry – Vectors and Translations (C)
Name: _______________________
Hour: ______
1. Name the vector and write its component form.
U P
2.
Liam is playing a battleship game against Maddie. The board shown below is Maddie’s board. Liam takes his first shot with a location of I3, which is a miss. a. If Liam moves his next shot to the right 4 and up 1 from his initial shot, will it be a hit or a miss? b. If Liam moves his next shot 〈3, −2〉 from his initial shot, will it be a hit or a miss? c. If Liam moves his next shot (𝑥, 𝑦) → (𝑥 − 1, 𝑦 + 5) from his initial shot, will it be a hit or a miss? d. Describe the how Liam needs to change his next shot from his initial shot to hit the location C8 in the following forms: Describe in Words Component Form Write a Rule
3. Point 𝐴(−4,0) is translated to Point 𝐴′(5,1). Graph the two points and write a rule for the translation.
4. Point 𝐷′ (−3, −2) was translated using the rule (𝑥, 𝑦) → (𝑥 − 3, 𝑦). What are the coordinates of the preimage?
5. Complete the table of the translation in all 4 representations: Show on a Graph Describe in Words
W
S
U
Write a Rule
Component Form
(𝑥, 𝑦) → (𝑥 + 4, 𝑦 − 3)
6. Draw line segment ̅̅̅̅ 𝐴𝐵 with points 𝐴(2,5) and 𝐵(1,0). If ̅̅̅̅ to ̅̅̅̅̅̅ you translate 𝐴𝐵 𝐴′𝐵′ using the component form 〈2,1〉, where will point 𝐴′ and point 𝐵′ be on the coordinate plane?
7. If you were to draw in the two vectors that translate 𝐴 to 𝐴’ and 𝐵 to 𝐵’, what shape would you create? Justify your answer.
Geometry – Vectors and Translations (D)
Name: _______________________
Hour: ______
1. Name the vector and write its component form. T
V
2.
Liam is playing a battleship game against Maddie. The board shown below is Maddie’s board. Liam takes his first shot with a location of I5, which is a miss. a. If Liam moves his next shot to the right 4 and up 1 from his initial shot, will it be a hit or a miss? b. If Liam moves his next shot 〈3, −2〉 from his initial shot, will it be a hit or a miss? c. If Liam moves his next shot (𝑥, 𝑦) → (𝑥 − 1, 𝑦 + 5) from his initial shot, will it be a hit or a miss? d. Describe the how Liam needs to change his next shot from his initial shot to hit the location C8 in the following forms: Describe in Words Component Form Write a Rule
3. Point 𝐴(−6, −2) is translated to Point 𝐴′(5,1). Graph the two points and write a rule for the translation.
4. Point 𝐷′ (−4,7) was translated using the rule (𝑥, 𝑦) → (𝑥 − 3, 𝑦). What are the coordinates of the preimage?
5. Complete the table of the translation in all 4 representations: Show on a Graph Describe in Words
W
S
U W’
S'
Write a Rule
U’
Component Form
6. Draw line segment ̅̅̅̅ 𝐴𝐵 with points 𝐴(2,5) and 𝐵(1,0). If ̅̅̅̅ to ̅̅̅̅̅̅ you translate 𝐴𝐵 𝐴′𝐵′ using the component form 〈6, −1〉, where will point 𝐴′ and point 𝐵′ be on the coordinate plane?
7. If you were to draw in the two vectors that translate 𝐴 to 𝐴’ and 𝐵 to 𝐵’, what shape would you create? Justify your answer.
Name: _______________________
Hour: ______
1. Name the vector and write its component form. B
M
2.
Liam is playing a battleship game against Maddie. The board shown below is Maddie’s board. Liam takes his first shot with a location of H3, which is a miss. a. If Liam moves his next shot to the right 4 and up 1 from his initial shot, will it be a hit or a miss? b. If Liam moves his next shot 〈3, −2〉 from his initial shot, will it be a hit or a miss? c. If Liam moves his next shot (𝑥, 𝑦) → (𝑥 − 1, 𝑦 + 5) from his initial shot, will it be a hit or a miss? d. Describe the how Liam needs to change his next shot from his initial shot to hit the location C8 in the following forms: Describe in Words Component Form Write a Rule
3. Point 𝐴(3,8) is translated to Point 𝐴′(5,1). Graph the two points and write a rule for the translation.
4. Point 𝐷′ (3, −1) was translated using the rule (𝑥, 𝑦) → (𝑥 − 3, 𝑦). What are the coordinates of the preimage?
5. Complete the table of the translation in all 4 representations: Show on a Graph Describe in Words
W
S
Write a Rule
U
∆𝑊𝑆𝑈 is translated 7 units to the right and 4 units down.
Component Form
6. Draw line segment ̅̅̅̅ 𝐴𝐵 with points 𝐴(2,5) and 𝐵(1,0). If ̅̅̅̅ to ̅̅̅̅̅̅ you translate 𝐴𝐵 𝐴′𝐵′ using the component form 〈−2,3〉, where will point 𝐴′ and point 𝐵′ be on the coordinate plane?
7. If you were to draw in the two vectors that translate 𝐴 to 𝐴’ and 𝐵 to 𝐵’, what shape would you create? Justify your answer.
Geometry – Vectors and Translations (B)
Name: _______________________
Hour: ______
1. Name the vector and write its component form. T
P
2.
Liam is playing a battleship game against Maddie. The board shown below is Maddie’s board. Liam takes his first shot with a location of H4, which is a miss. a. If Liam moves his next shot to the right 4 and up 1 from his initial shot, will it be a hit or a miss? b. If Liam moves his next shot 〈3, −2〉 from his initial shot, will it be a hit or a miss? c. If Liam moves his next shot (𝑥, 𝑦) → (𝑥 − 1, 𝑦 + 5) from his initial shot, will it be a hit or a miss? d. Describe the how Liam needs to change his next shot from his initial shot to hit the location C8 in the following forms: Describe in Words Component Form Write a Rule
3. Point 𝐴(2,6) is translated to Point 𝐴′(5,1). Graph the two points and write a rule for the translation.
4. Point 𝐷′ (6, −1) was translated using the rule (𝑥, 𝑦) → (𝑥 − 3, 𝑦). What are the coordinates of the preimage?
5. Complete the table of the translation in all 4 representations: Show on a Graph Describe in Words
W
S
Write a Rule
U
Component Form 〈−2, −5〉
6. Draw line segment ̅̅̅̅ 𝐴𝐵 with points 𝐴(2,5) and 𝐵(1,0). If ̅̅̅̅ to ̅̅̅̅̅̅ you translate 𝐴𝐵 𝐴′𝐵′ using the component form 〈6,3〉, where will point 𝐴′ and point 𝐵′ be on the coordinate plane?
7. If you were to draw in the two vectors that translate 𝐴 to 𝐴’ and 𝐵 to 𝐵’, what shape would you create? Justify your answer.
Geometry – Vectors and Translations (C)
Name: _______________________
Hour: ______
1. Name the vector and write its component form.
U P
2.
Liam is playing a battleship game against Maddie. The board shown below is Maddie’s board. Liam takes his first shot with a location of I3, which is a miss. a. If Liam moves his next shot to the right 4 and up 1 from his initial shot, will it be a hit or a miss? b. If Liam moves his next shot 〈3, −2〉 from his initial shot, will it be a hit or a miss? c. If Liam moves his next shot (𝑥, 𝑦) → (𝑥 − 1, 𝑦 + 5) from his initial shot, will it be a hit or a miss? d. Describe the how Liam needs to change his next shot from his initial shot to hit the location C8 in the following forms: Describe in Words Component Form Write a Rule
3. Point 𝐴(−4,0) is translated to Point 𝐴′(5,1). Graph the two points and write a rule for the translation.
4. Point 𝐷′ (−3, −2) was translated using the rule (𝑥, 𝑦) → (𝑥 − 3, 𝑦). What are the coordinates of the preimage?
5. Complete the table of the translation in all 4 representations: Show on a Graph Describe in Words
W
S
U
Write a Rule
Component Form
(𝑥, 𝑦) → (𝑥 + 4, 𝑦 − 3)
6. Draw line segment ̅̅̅̅ 𝐴𝐵 with points 𝐴(2,5) and 𝐵(1,0). If ̅̅̅̅ to ̅̅̅̅̅̅ you translate 𝐴𝐵 𝐴′𝐵′ using the component form 〈2,1〉, where will point 𝐴′ and point 𝐵′ be on the coordinate plane?
7. If you were to draw in the two vectors that translate 𝐴 to 𝐴’ and 𝐵 to 𝐵’, what shape would you create? Justify your answer.
Geometry – Vectors and Translations (D)
Name: _______________________
Hour: ______
1. Name the vector and write its component form. T
V
2.
Liam is playing a battleship game against Maddie. The board shown below is Maddie’s board. Liam takes his first shot with a location of I5, which is a miss. a. If Liam moves his next shot to the right 4 and up 1 from his initial shot, will it be a hit or a miss? b. If Liam moves his next shot 〈3, −2〉 from his initial shot, will it be a hit or a miss? c. If Liam moves his next shot (𝑥, 𝑦) → (𝑥 − 1, 𝑦 + 5) from his initial shot, will it be a hit or a miss? d. Describe the how Liam needs to change his next shot from his initial shot to hit the location C8 in the following forms: Describe in Words Component Form Write a Rule
3. Point 𝐴(−6, −2) is translated to Point 𝐴′(5,1). Graph the two points and write a rule for the translation.
4. Point 𝐷′ (−4,7) was translated using the rule (𝑥, 𝑦) → (𝑥 − 3, 𝑦). What are the coordinates of the preimage?
5. Complete the table of the translation in all 4 representations: Show on a Graph Describe in Words
W
S
U W’
S'
Write a Rule
U’
Component Form
6. Draw line segment ̅̅̅̅ 𝐴𝐵 with points 𝐴(2,5) and 𝐵(1,0). If ̅̅̅̅ to ̅̅̅̅̅̅ you translate 𝐴𝐵 𝐴′𝐵′ using the component form 〈6, −1〉, where will point 𝐴′ and point 𝐵′ be on the coordinate plane?
7. If you were to draw in the two vectors that translate 𝐴 to 𝐴’ and 𝐵 to 𝐵’, what shape would you create? Justify your answer.
