🎯 Learning Targets & Supports

I can... identify and analyze translations using vectors, compute image coordinates, and explain how translations affect 2D and 3D objects.

Success criteria: I can (1) write a translation vector, (2) apply a vector to coordinates correctly, and (3) justify whether translations change size, area, or volume.

Differentiation: Provide grid paper or color-coded coordinates for students who need visual supports; offer step-by-step templates for computation.

Extension: Apply translations to a composite figure or consider translations of 3D nets and explain effects on surface area and volume.

Dyslexia-friendly option: Use larger fonts, increased spacing, and high-contrast colors on printed copies; read problems aloud when needed.

📚 Part 1: Multiple Choice & Quick Checks

1. A translation in the plane is a:

rotation about the origin

reflection across a line

slide that moves every point by the same vector

change in size (dilation)

2. Translate point (2, 4) by the vector <3, −1>. The image is:

(5, 3)

(5, 5)

(−1, 3)

(2, 3)

3. Check all that apply: A translation

preserves shape and size

preserves orientation

changes distances between points

requires a rotation

4. Triangle with vertices A(1,2), B(4,2), C(1,5) is translated by <−2, −1>. Vertex B' is:

(2, 1)

(6, 3)

(2, 3)

(−1, 1)

5. True or False: Translations can change the area of a 2D figure.

True

False

✏️ Part 2: Short Answer, Matching, & Analysis

6. Write the translation vector that maps P(−1, 3) to P'(4, −2):

7. Calculate the image of the point (3, 1) under the translation <0, 6>. Show your work:

8. Match each pre-image point (left) to its image after translation by <2, −3> (right). Draw lines or write pairs.

A. (−2, 5)

B. (0, 0)

C. (3, −1)

D. (1, 4)

(3, 1)

(5, −4)

(2, −3)

(0, 2)

9. Explain in one sentence how translations relate to surface area and volume for 3D objects. (Hint: think about moving an object without rotating or resizing it.)

10. Optional: Sketch a pre-image and its translation by <4, −2> on the grid below (use the box if printing):