Coordinate Translations Worksheet
Geometry Skills Practice
Translations on the Coordinate Plane
Name:
Date:
Period:
Directions: Write a rule to describe each transformation from the pre-image (black) to the image (blue).
Page 1 (1–5)
1 TUV → T'U'V'
x y T U V T' U' V'
Atranslation: 3 units left and 2 units down
Btranslation: 2 units left and 2 units down
Ctranslation: 3 units left and 2 units up
Dtranslation: 6 units left
2 EFG → E'F'G'
x y E F G E' F' G'
Atranslation: 1 unit left and 1 unit down
Btranslation: 5 units left and 2 units up
Ctranslation: 1 unit left and 3 units up
Dtranslation: 5 units left
3 JKL → J'K'L'
x y J K L J' K' L'
Atranslation: 4 units down
Btranslation: 7 units right and 1 unit up
Ctranslation: 4 units right and 5 units down
Dtranslation: 6 units right
4 BCD → B'C'D'
x y B C D B' C' D'
Atranslation: 5 units up
Btranslation: 1 unit right and 2 units up
Ctranslation: 1 unit right
Dtranslation: 3 units left and 5 units up
5 EFG → E'F'G'
x y E F G E' F' G'
Atranslation: 2 units right and 2 units down
Btranslation: 4 units right and 6 units down
Ctranslation: 4 units right and 1 unit down
Dtranslation: 4 units right and 2 units down
Translation Reference Key
A translation slides every vertex of a figure the exact same distance and direction.
Pre-Image vs. Image:
Always count from original point (e.g., \(T\)) to prime point (e.g., \(T'\)).
Horizontal & Vertical Rules:
• Right: \(x + a\)
• Left: \(x - a\)
• Up: \(y + b\)
• Down: \(y - b\)
Coordinate Notation: \((x, y) \rightarrow (x \pm a, y \pm b)\)
Translations Practice Worksheet Page 1 of 2
Geometry Skills Practice
Translations on the Coordinate Plane
Name:
Part 2
Directions: Continue identifying the translation rule from the pre-image to the image.
Page 2 (6–10)
6 GHI → G'H'I'
x y G H I G' H' I'
Atranslation: 5 units right
Btranslation: 6 units up
Ctranslation: 2 units right and 1 unit up
Dtranslation: 3 units right and 1 unit up
7 EFG → E'F'G'
x y E F G E' F' G'
Atranslation: 4 units left and 2 units up
Btranslation: 4 units left
Ctranslation: 4 units left and 3 units up
Dtranslation: 3 units left and 1 unit up
8 QRS → Q'R'S'
x y Q R S Q' R' S'
Atranslation: 4 units right and 1 unit down
Btranslation: 4 units right and 7 units down
Ctranslation: 4 units right and 5 units down
Dtranslation: 5 units right and 6 units down
9 RST → R'S'T'
x y R S T R' S' T'
Atranslation: 3 units right and 1 unit down
Btranslation: 2 units right
Ctranslation: 4 units right and 1 unit down
Dtranslation: 1 unit left
10 QRS → Q'R'S'
x y Q R S Q' R' S'
Atranslation: 2 units left and 7 units up
Btranslation: 3 units left and 7 units up
Ctranslation: 1 unit left and 1 unit down
Dtranslation: 4 units left and 2 units up
Algebraic Rule Challenge
Extension
Write mapping notation \((x, y) \rightarrow (x \pm a, y \pm b)\) for the indicated problems:
Problem #1 Rule:
(x, y) → ( )
Problem #8 Rule:
(x, y) → ( )
Critical Thinking:
Which coordinate value changes when a shape moves only left or right?
Answer:
Coordinate geometry transformation practice
Translations Practice Worksheet Page 2 of 2
Coordinate Translations Answer Key
Teacher Key Full Solutions & Vectors
Translations on the Coordinate Plane
Quick Key (1–5):
1: B | 2: D | 3: A | 4: D | 5: D
Visual Solutions: Red dashed vector arrows show the exact displacement from pre-image vertex to image vertex.
Page 1 (1–5)
1 Correct: B
\(\langle -2, -2 \rangle\)
TUV T'U'V'
A) 3 units left and 2 units down
✓ B) translation: 2 units left and 2 units down (x-2, y-2)
C) 3 units left and 2 units up
D) 6 units left
2 Correct: D
\(\langle -5, 0 \rangle\)
EFG E'F'G'
A) 1 unit left and 1 unit down
B) 5 units left and 2 units up
C) 1 unit left and 3 units up
✓ D) translation: 5 units left (x-5, y)
3 Correct: A
\(\langle 0, -4 \rangle\)
JKL J'K'L'
✓ A) translation: 4 units down (x, y-4)
B) 7 units right and 1 unit up
C) 4 units right and 5 units down
D) 6 units right
4 Correct: D
\(\langle -3, +5 \rangle\)
BCD B'C'D'
A) 5 units up
B) 1 unit right and 2 units up
C) 1 unit right
✓ D) translation: 3 units left and 5 units up (x-3, y+5)
5 Correct: D
\(\langle +4, -2 \rangle\)
EFG E'F'G'
A) 2 units right and 2 units down
B) 4 units right and 6 units down
C) 4 units right and 1 unit down
✓ D) translation: 4 units right and 2 units down (x+4, y-2)
Grading & Error Diagnostics
Common misconceptions observed when students assess translations:
1. Reversing Direction (Pre-Image ↔ Image):
Students often mistakenly count from the prime figure to the original (e.g., picking 2 right, 2 up in #1 instead of 2 left, 2 down).
2. Inverting Axes (\(x\) vs. \(y\)):
Remind students to always state horizontal movement (left/right) first, matching the \(x\)-coordinate in ordered pairs.
Scoring suggestion: 1 pt per correct option (10 pts total)
Teacher Answer Key • Translations Practice Page 1 of 2
Teacher Key Full Solutions & Vectors
Translations on the Coordinate Plane
Quick Key (6–10):
6: D | 7: A | 8: C | 9: B | 10: D
Visual Solutions: Continue identifying vectors and check the model answers for the extension challenge.
