Activity: Understanding Translations Using Vectors (GeoGebra)

Auteur :Kateryne Ramos Cedeño, Sonam Zangmo

Part 1: Perform the Translation

1. Move the slider so that a=1

2. Drag the points A, B, and C to explore how the triangle changes.

3. Observe the image of the triangle: A′, B′, and C′.

1.1 Exploration Question

After moving the slider to a=1 and dragging the points A, B, and C: What characteristics do you observe about triangle ABC and its image A′,B′,C′? Write your answer using mathematical language. Consider:

The shape and size of the triangle
The orientation of the figure
The distance and direction each point moves

Horizontal and Vertical Movement on the Coordinate Plane

On the coordinate plane, a point can move in two ways:

Horizontal movement (x): to the right or to the left
Vertical movement (y): up or down

Example Suppose point A(-2,1) moves to B(2,4) Step 1: Horizontal movement From x=-2 to x=2: It moves 4 units to the right Step 2: Vertical movement From y=1 to y=4: It moves 3 units down

2. Coordinate-Based Question

Place the points A(−4,2), B(−2,3), and C(-2, 1) on the coordinate plane, and the slider to a=1.

2.1 Then observe their images A′, B′, and C′.

How many units does each point move horizontally and vertically to reach its image?

Count the number of grid squares from A to A′:

Cochez votre réponse ici

A
6
B
-6
C
3
D
-3

2.2 Then observe their images A′, B′, and C′.

How many units does each point move vertically to reach its image?

Count the number of grid squares from A to A′: