Lesson 1
What would this (A’) be called?
A-prime
What is an example of a transformation that turns?
Rotation
What does CW and CCW stand for?
Clockwise and counterclockwise
Reflection: The picture shows that the size of the figure ________, the orientation of the figure ______ and the orientation of the vertices _______ also.
The picture shows that the size of the figure stayed the same, the orientation of the figure changed and the orientation of the vertices changed also.
What are the two types of axis’s called?
X and y axis
What are the 4 types of Transformations?
Translation, Rotation, Reflection and Dilation
Describe the translations for all three problems:
1. N(-6,-8) ➡️ N’(-5,2)
2. M(12,7) ➡️ M’(-1,14)
3. O(-3,6) ➡️ O’(-9,-1)
1. 1 unit right, 10 up
2. 13 units left, 7 units up
3. 6 units left, 7 units down
The coordinates below represent rotations. Use what you’re learned today to describe what type of rotation occurred.
1. X (9,8) ➡️ X’ (8,-9)
2. Y (-4,5) ➡️ Y’ (-5,-4)
3. Z (-6,-1) ➡️ (6,1)
1. 90 degrees clockwise or 270 degrees counterclockwise
2. 270 degrees clockwise or 90 degrees counterclockwise
3. 180 degrees clockwise or 180 degrees counterclockwise
Translate the figure 5 units left and 2 units down. Record the coordinates of the pre-image and image in the table.
Answer:
Pre-image: A(2,4) B(6,7) C(7,3)
Image: A’(-3,2) B’(1,5) C’(2,1)
The x value decreased by 5 and the y value decreased by 2.
What is the definition for Translation?
Translation - moves/slides
The shape or figure before the transformation is called what?
Pre-image
Refers to the order in which the vertices are labeled, clockwise or counterclockwise. What is this called?
Orientation of the Vertices
What is the algebraic representation 90 degrees clockwise (270 degrees counterclockwise)?
Pre-image: A(2,1) B(6,1) C’(4,7) Image: A’(1,-2) B’(1,-6) C’(7,-4)
(y , -x)
The x and y coordinates switch, x becomes the opposite sign.
A rotation _____ a figure around a fixed point called the center of _________.
For our examples, the center of rotation will be the _____ and we’ll rotate in increments of _____ degrees.
A rotation turns a figure around a fixed point called the center of rotation.
For our examples, the center of rotation will be the origin and we’ll rotate in increments of 90 degrees.
What is the definition for Reflection?
Reflection - mirror image
The shape or figure after the transformation is called what?
Image
Whether or not the figure is facing the same direction on the the coordinate plane after transformation. What is this?
Orientation of the figure
What is the algebraic representation for 180 degrees clockwise (180 degrees counterclockwise)?
Pre-image: A(2,1) B(6,1) C(4,7)
Image: A’(-2,-1) B’(-6,-1) C’(-4,-7)
(-x , -y)
The x and y coordinates become the opposite sign.
What is the definition for Rotation?
Rotation - turn around
Whether or not a figure has the same size and shape after transformation. What is this?
Congruence
What is the reflection over the x and y axis?
Reflection over x-axis: X - stays the same
Y - flips the sign Reflection over y-axis:
X - flips the sign
Y - stay the same
What is the definition for Dilation?