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Rigid Transformations
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1. Reflections on the Coordinate Plane
- Reflections on the Coordinate Plane
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2. Rotations on the Coordinate Plane
- Rotations on the Coordinate Plane
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3. Translations on the Coordinate Plane
- Translations on the Coordinate Plane
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Rigid Transformations
Gabriela Sanchez, Nov 14, 2018
Table of Contents
- Reflections on the Coordinate Plane
- Reflections on the Coordinate Plane
- Rotations on the Coordinate Plane
- Rotations on the Coordinate Plane
- Translations on the Coordinate Plane
- Translations on the Coordinate Plane
Reflections on the Coordinate Plane
Answer the following questions in your notes.
Activity 1: Reflecting Over the x - axis
Move points J and K so that they lie on the x - axis.
1) Click and drag Triangle ABC. Change the size of Triangle ABC. What do you notice bout the size and shape of Triangle A'B'C'?
2) State the coordinates of Triangle ABC and the coordinates of Triangle A'B'C'.
A (___,____) --> A' (___,____)
B (___,____) --> B' (___,____)
C (___,____) --> C' (___,____)
3) What changes in the coordinate(s) do you notice when reflecting over the x - axis?
4) Fill in the blanks.
BIG IDEA: When reflecting across the x - axis, the _________ coordinate changes ______________.
Activity 2: Reflecting Over the y - axis
Move points J and K so that they lie on the y - axis.
1) Click and drag Triangle ABC. Change the size of Triangle ABC. What do you notice bout the size and shape of Triangle A'B'C'?
2) State the coordinates of Triangle ABC and the coordinates of Triangle A'B'C'.
A (___,____) --> A' (___,____)
B (___,____) --> B' (___,____)
C (___,____) --> C' (___,____)
3) What changes in the coordinate(s) do you notice when reflecting over the y - axis?
4) Fill in the blanks.
BIG IDEA: When reflecting across the y - axis, the _________ coordinate changes ______________.
Activity 3: Reflecting Over the Line y =x
Move Points J to the coordinates (1,1). Move Point K to the coordinates (3,3).
1) Click and drag Triangle ABC. Change the size of Triangle ABC. What do you notice bout the size and shape of Triangle A'B'C'?
2) State the coordinates of Triangle ABC and the coordinates of Triangle A'B'C'.
A (___,____) --> A' (___,____)
B (___,____) --> B' (___,____)
C (___,____) --> C' (___,____)
3) What changes in the coordinate(s) do you notice when reflecting over the line y = x?
4) Fill in the blanks.
BIG IDEA: When reflecting across the y = x, the _________ & ____________ coordinate change ___________________.
Rotations on the Coordinate Plane
Answer the following questions in your notes.
Click and drag the scale to change the degree of rotation.
1) Point O is the point of rotation. Its coordinates are (0,0). What is the name for the point at (0,0)?
2) When the degree of rotation is 0 or 360, what do you notice about the position of Triangle ABC and Triangle A'B'C'?
3) Click and drag the degree of rotation to 180 degrees. Change the size of Triangle ABC. What do you notice about the size and shape of Triangle A'B'C'?
4) State the coordinates of Triangle ABC and the coordinates of Triangle A'B'C'.
A (___,____) --> A' (___,____)
B (___,____) --> B' (___,____)
C (___,____) --> C' (___,____)
5) What changes in the coordinate(s) do you notice when you rotate 180 degrees about the origin?
4) Fill in the blanks.
BIG IDEA: When rotating 180 degrees about the origin, the _________ and _________ coordinate change ______________.
Translations on the Coordinate Plane
Answer the following questions in your notes.
Click and drag the Points J and K to change the length and direction of vector.
1) Click and drag the Points J and K. Change the length of the vector. What do you notice happens between Triangle ABC and Triangle A'B'C'?
2) Click on K and change the direction of the vector. What do you notice happens between Triangle ABC and Triangle A'B'C'?
3) Change the size of Triangle ABC. What do you notice about the size and shape of Triangle A'B'C'?
4) Record the slope of the vector.
Slope is _____________.
5) State the coordinates of Triangle ABC and the coordinates of Triangle A'B'C'.
A (___,____) --> A' (___,____)
B (___,____) --> B' (___,____)
C (___,____) --> C' (___,____)
6) What do you notice between the slope of the vector and how the coordinates of Triangle ABC and the coordinates of Triangle A'B'C' relate to each other?
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