Translation Vector Practice

Name:

Date:

Coordinate grid with arrow showing translation

📍 Part 1: Understanding Translation Vectors

1. What does the vector (4, -2) tell us about a translation?

Move 4 units up and 2 units left

Move 4 units right and 2 units down

Move 4 units left and 2 units up

Move 4 units down and 2 units right

2. A point at (3, 5) is translated by vector (-2, 3). What is its new position?

(1, 8)

(5, 2)

(-2, 3)

(1, 2)

3. Which properties remain unchanged when a shape is translated? (Select all that apply)

Size

Shape

Position

Orientation

📐 Part 2: Working with Coordinates

4. Triangle ABC has vertices at A(2, 1), B(4, 1), and C(3, 4). If it's translated by vector (5, -2), write the new coordinates:

A' = ( _____ , _____ )

B' = ( _____ , _____ )

C' = ( _____ , _____ )

5. A rectangle is translated from position PQRS to position P'Q'R'S'. If P(1, 2) moves to P'(4, 7), what is the translation vector?

6. Complete the rule: Under translation by vector (a, b), the point (x, y) maps to:

( _____ , _____ )

7. Show your working to find where the point (-3, 6) moves when translated by vector (7, -4):

🎯 Part 3: Real-World Applications

8. A video game character starts at position (10, 15) on the screen. The player moves the character 8 units left and 3 units up. Write the translation vector and find the character's new position.

Translation vector: ( _____ , _____ )

New position: ( _____ , _____ )

9. Explain in your own words why translation is called a "rigid transformation" and give one real-world example where translation occurs:

10. On a coordinate grid, sketch how you would show the translation of a tapatoru (triangle) by vector (3, 2). Label your original and translated shapes clearly.