Coordinate Translations Worksheet
Geometry • Coordinate Plane
Coordinate Translations
Find the coordinates of the vertices of each figure after the given transformation.
Name:
Date: Period:
1 7 units left and 6 units up
x y G
Pre-image: G(4, −3)
A G'(−3, −4)
B G'(−3, 3)
C G'(−5, −3)
D G'(−4, 1)
Rule: (x − 7, y + 6) Answer: [ ]
2 5 units down
x y P
Pre-image: P(1, 0)
A P'(−2, −2)
B P'(−2, −5)
C P'(1, −5)
D P'(3, −2)
Rule: (x, y − 5) Answer: [ ]
3 2 units left and 3 units down
x y J
Pre-image: J(−1, −1)
A J'(3, 1)
B J'(−3, −4)
C J'(5, 4)
D J'(3, 0)
Rule: (x − 2, y − 3) Answer: [ ]
4 4 units left and 4 units down
x y Y
Pre-image: Y(−1, 2)
A Y'(−5, −2)
B Y'(3, 4)
C Y'(3, 2)
D Y'(−4, −5)
Rule: (x − 4, y − 4) Answer: [ ]
5 3 units right
x y J
Pre-image: J(−1, 2)
A J'(5, −5)
B J'(−3, 1)
C J'(−5, −3)
D J'(2, 2)
Rule: (x + 3, y) Answer: [ ]
Translation Coordinate Rules
Right h units • Left h units x ± h
Up k units • Down k units y ± k
Transformation Notation:
(x, y) → (x + a, y + b)
Add for right/up; subtract for left/down.
Coordinate Translations • Geometry Practice Page 1 of 2
Coordinate Translations
Continue finding image coordinates after each translation.
Problems 6 – 10 + Extension
6 3 units right and 1 unit up
x y L
Pre-image: L(−2, −1)
A L'(1, 0)
B L'(1, −2)
C L'(−5, −5)
D L'(1, −5)
Rule: (x + 3, y + 1) Answer: [ ]
7 1 unit right and 3 units up
x y L
Pre-image: L(−2, 0)
A L'(−3, 1)
B L'(−1, 3)
C L'(3, 5)
D L'(5, −2)
Rule: (x + 1, y + 3) Answer: [ ]
8 5 units left and 4 units down
x y U
Pre-image: U(4, 5)
A U'(4, 4)
B U'(3, −5)
C U'(2, −5)
D U'(−1, 1)
Rule: (x − 5, y − 4) Answer: [ ]
9 5 units left and 6 units down
x y U
Pre-image: U(4, 5)
A U'(−1, −1)
B U'(−4, 1)
C U'(4, 0)
D U'(−3, 3)
Rule: (x − 5, y − 6) Answer: [ ]
10 2 units right and 6 units down
x y V
Pre-image: V(3, 2)
A V'(−2, −4)
B V'(−4, −1)
C V'(3, −1)
D V'(5, −4)
Rule: (x + 2, y − 6) Answer: [ ]
Challenge • Reverse Translation Bonus
A mystery point T was translated 4 units left and 5 units up, landing at the image T'(1, −2).
What were the coordinates of the original point T?
Reverse the rule: T( _____ , _____ )
Tip: To find the pre-image from the image, perform the opposite operation!
Coordinate Translations • Geometry Practice Page 2 of 2
Coordinate Translations Answer Key
Teacher Solution Guide • Answer Key
Coordinate Translations • Page 1 Answers
Step-by-step vector arithmetic and plotted transformations for items 1 – 5.
Quick Key (1–5)
1: B 2: C 3: B 4: A 5: D
KEY: B
1 7 units left & 6 units up
G G'
G(4, −3) → (4 − 7, −3 + 6)
= G'(−3, 3)
A) G'(−3, −4)
✓ B) G'(−3, 3)
C) G'(−5, −3)
D) G'(−4, 1)
KEY: C
2 5 units down
P P'
P(1, 0) → (1, 0 − 5)
= P'(1, −5)
A) P'(−2, −2)
B) P'(−2, −5)
✓ C) P'(1, −5)
D) P'(3, −2)
KEY: B
3 2 units left & 3 units down
J J'
J(−1, −1) → (−1 − 2, −1 − 3)
= J'(−3, −4)
A) J'(3, 1)
✓ B) J'(−3, −4)
C) J'(5, 4)
D) J'(3, 0)
KEY: A
4 4 units left & 4 units down
Y Y'
Y(−1, 2) → (−1 − 4, 2 − 4)
= Y'(−5, −2)
✓ A) Y'(−5, −2)
B) Y'(3, 4)
C) Y'(3, 2)
D) Y'(−4, −5)
KEY: D
5 3 units right
J J'
J(−1, 2) → (−1 + 3, 2)
= J'(2, 2)
A) J'(5, −5)
B) J'(−3, 1)
C) J'(−5, −3)
✓ D) J'(2, 2)
Common Student Misconceptions
- Reversing Axes: Applying horizontal shifts to the y-coordinate or vertical shifts to the x-coordinate.
- Integer Sign Errors: Adding instead of subtracting when moving left or down (e.g., in #4 calculating −1 + 4 = 3 instead of −1 − 4 = −5).
- Single Shift Neglect: In #2 and #5, changing both coordinates when only one direction was specified.
Grading Recommendation: 10 points (1 point per item). Award partial credit if rule is correctly written but arithmetic has sign error.
Coordinate Translations • Teacher Solution Key Page 1 of 2
Coordinate Translations • Page 2 Answers
Step-by-step vector arithmetic and plotted transformations for items 6 – 10.
Quick Key (6–10)
6: A 7: B 8: D 9: A 10: D
KEY: A
