Activity: Understanding Translations Using Vectors (GeoGebra)

Part 1: Perform the Translation
[*]1. Move the slider so that a=1[/*][*][br]2. Drag the points A, B, and C to explore how the triangle changes.[/*][*][br]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:[br][br][b]What characteristics do you observe about triangle ABC and its image A′,B′,C′?[/b][br][br]Write your answer using mathematical language. Consider:[list][*]The shape and size of the triangle[br][/*][*]The orientation of the figure[br][/*][*]The distance and direction each point moves[/*][/list]
Horizontal and Vertical Movement on the Coordinate Plane
On the coordinate plane, a point can move in two ways:[br][list][*][b]Horizontal movement (x):[/b] to the right or to the left[br][/*][*][b]Vertical movement (y):[/b] up or down[/*][/list][b][br]Example[/b][br]Suppose point A(-2,1) moves to B(2,4)[br][br][b]Step 1: Horizontal movement[/b][br] From x=-2 to x=2:[br] It moves [b]4 units to the right[/b][br][br][b]Step 2: Vertical movement[/b][br] From y=1 to y=4:[br] It moves [b]3 units down[br][br][/b][img]data:image/png;base64,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[/img]
2. Coordinate-Based Question
[br]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′.
[b]How many units does each point move horizontally and vertically to reach its image?[/b][br][list][*]Count the number of grid squares from A to A′:[/*][/list]
2.2 Then observe their images A′, B′, and C′.
[b]How many units does each point move [b]vertically[/b] to reach its image?[br][/b][br][list][*]Count the number of grid squares from A to A′:[/*][/list]

Understanding Rotations Using Angles (GeoGebra)

Rotation
The example below shows a rotation about the origin of triangle ABC. [br]Move the slider to see how triangle A'B'C' rotates. [br]
1. How does the rotation affect the triangle A'B'C'? [br][br]2. Is triangle ABC and triangle A'B'C' always congruent?[br][br]Challenge: Is there a way reflections could be used to get triangle ABC on A'B'C'.

Informaţie