Vector Voyages Slides Geometry Unit 4
VECTOR VOYAGES
Mastering the Art of the Slide
Slide
Translate
Rigid Motion
What is a Translation?
A translation is a transformation that slides every point of a figure the same distance in the same direction.
Think of it as a "SLIDE" .
The figure does not turn or flip.
The figure stays the same size.
START
END
Rule of the Road
Algebraic Notation
(x, y) → (x + h, y + k)
x
Left or Right
+ Moves Right
- Moves Left
y
Up or Down
+ Moves Up
- Moves Down
Example: Step-by-Step
1
Identify Rule
Let's move right 3 and down 2.
(x+3, y-2)
2
Pick a Point
Point A is at (1, 5).
A(1, 5)
3
Calculate
Add 3 to x. Subtract 2 from y.
A'(4, 3)
Is it a Translation?
YES
Same size. Same face.
NO
It turned (rotated)!
Translation Practice Packet VECTOR VOYAGES
Translation Practice Packet
Name:
Date:
The Navigation Guide
Horizontal Movement (x)
(x + h) : Move Right(x - h) : Move Left
Vertical Movement (y)
(y + k) : Move Up(y - k) : Move Down
Part 1: Key Terms
Word Bank
Translation Pre-Image Image Rigid Motion
The original figure before any change is called the
.
A slide that moves every point the same distance is a
.
The figure after the transformation is called the
.
Part 2: Visual Check
Circle "YES" if the move is a translation (slide) and "NO" if it is not.
4
YES
NO
5
YES
NO
6
YES
NO
Part 3: Coordinate Rules
Find the new coordinates of point A' (the image) using the given rule.
7
Pre-Image: A (2, 4)
Rule: (x + 3, y - 5)
Your Work:
x: 2 + 3 =
y: 4 - 5 =
A' (
,
)
8
Pre-Image: B (-3, 1)
Rule: (x - 2, y + 6)
Space for work
B' (
,
)
Part 4: Plot the Move
Translate Triangle ABC using the rule: Move Right 4 units and Down 3 units.
A B C
Final Step: Record Coordinates
Pre-Image (Start):
A (-2, 2)
B (0, 2)
C (-2, 0)
Image (After Slide):
A' (
,
)
B' (
,
)
C' (
,
)
Vector Voyages Answer Key ANSWER KEY
Vector Voyages: Practice Packet
Teacher Resource
Part 1: Key Terms
1. The original figure before any change is called the Pre-Image.
2. A slide that moves every point the same distance is a Translation.
3. The figure after the transformation is called the Image.
Part 2: Visual Check
YES Standard slide (rigid motion).
NO Rotation (the shape turned).
NO Dilation (the shape changed size).
Part 3: Coordinate Rules
Problem 7: (x+3, y-5) for A(2, 4)
A' (5, -1)
Problem 8: (x-2, y+6) for B(-3, 1)
B' (-5, 7)
Part 4: Graphing Answer
A' B' C'
Coordinate Key
Pre-Image
A (-2, 2)
B (0, 2)
C (-2, 0)
Image (A')
A' (2, -1)
B' (4, -1)
C' (2, -3)
Vector Voyages Facilitator Guide FACILITATOR GUIDE
Lesson: Vector Voyages (60 Minutes)
Teacher Resource
Subject
Geometry / Translations
Grade Level
High School (Modified)
Duration
60 Minutes
Learning Objectives
Identify translations as a "slide" transformation (rigid motion).
Apply algebraic rules \((x \pm h, y \pm k)\) to coordinate points.
Graph the image of a figure after a translation on a coordinate plane.
Pacing Schedule
00-05: Warm-Up (Quick Start Bell Ringer)
Students identify coordinates of points on a grid to activate prior knowledge of the x-y plane.
05-20: Direct Instruction (Vector Voyages Slides)
Introduce "Slide" terminology, rigid motion, and algebraic notation. Use visual examples to differentiate from rotation/dilation.
20-35: Guided Practice (Practice Packet - Page 1-2)
Complete the vocabulary and visual check sections as a class. Model the first coordinate rule problem.
35-50: Task Card Challenge (Group Activity)
Students work in pairs to solve 4-6 translation task cards around the room or at desks.
50-55: Independent Practice (Practice Packet - Page 3-4)
Students complete the remaining graphing and calculation problems independently.
55-60: Closure & Exit Ticket
Quick assessment: perform one translation and state the rule.
Modification & Differentiation Strategies
Visual Supports
Color Coding: Use blue for x-axis/horizontal moves and red for y-axis/vertical moves consistently.Graphic Organizer: Refer to the "Navigation Guide" in the packet for every problem.Arrow Anchors: Provide physical arrows for students to slide on their desk to mimic the movement.
Instructional Scaffolds
Think-Alouds: "I see a +4. My guide says + means right. I'm going to move my finger 4 spaces right."Reduced Workload: The packet is intentionally limited to 2-3 problems per page to prevent overwhelm.Peer Support: During the Task Card phase, pair students with a "Navigation Buddy."
Key Questions to Ask
"If we move a shape 5 units up, does its size change? Why or why not?"
"Which coordinate (x or y) do we change when we slide a figure left?"
"Look at point A and its image A'. How can we tell this was a slide and not a turn?"
Quick Start Bell Ringer QUICK START
Vector Voyages: Daily Warm-Up
Name:
Date:
Goal: Locate the Coordinates
Before we sail, we need to know where we are! Identify the (x, y) coordinates for each point below.
A B C
Point A:
(
,
)
Point B:
(
,
)
Point C:
(
,
)
Translation Task Cards VECTOR VOYAGES: TASK CARDS
Activity: Task Card Challenge
1
Pre-Image Point
P (4, 2)
Translation Rule:
(x + 5, y - 3)
Where is P' ?
Slide 5 Right, 3 Down
2
Pre-Image Point
Q (-1, 0)
Slide Rule:
Left 2 and Up 4
Find Point Q'
3
Look at the shapes.
YES
NO
4
Identify Rule
Point A (0,0) moves to A' (3, -2)
What is the rule?
(x+3, y-2)
(x-3, y+2)
TASK CARD LOG
Name:
1
Point P'
( ____ , ____ )
2
Point Q'
( ____ , ____ )
3
Check
YES
NO
4
Rule
(x ____ , y ____ )
Task Cards Answer Key TASK CARDS
Teacher Answer Key
Key
1
Point P' (9, -1)
Rule (x+5, y-3). Work: 4+5=9, 2-3=-1
2
Point Q' (-3, 4)
Rule (x-2, y+4). Work: -1-2=-3, 0+4=4
3
Answer: YES
The figure is a translation because size and orientation remained the same.
4
Rule: (x + 3, y - 2)
Move A(0,0) to A'(3,-2). Work: x+3, y-2
Voyage Log Exit Ticket VOYAGE LOG
Exit Ticket: Translation Check
Name:
You are given point Z (5, -2).
Apply the rule: (x - 4, y + 7)
1. What are the new coordinates for Z'?
( ____ , ____ )
2. Did the shape change size? (Circle one)
YES
NO
