Transformations Unit Flashcards
What are the 2 components of polar coordinates?
(r , ϴ ) - Radius and direction
What are the different types of transformations?
Translations, rotations, reflections and dilations
What is an isometry?
An isometry occurs when the transformed figure is congruent to the original one
Which transformations give an isometry?
Translations, rotations, and reflections
Which transformations do not give an isometry?
Dilations
When a dilation occurs, what is the relationship between the two figures?
They are similar
How do you define a translation?
T(x , y) = (x ± a , y ± b)
How do you define a rotation?
R(0 , ϴ)
How do you define a dilation?
D( P , k )
If D is at (x , y) and reflected about the y axis, what are the coordinates of D’?
(-x , y)
If F is at (x , y) and reflected about the x axis, what are the coordinates of F’?
(x , -y)
If H is at (x, y) and rotated by R(O,90°) what are the coordinates of H’?
(-y , x)
If I is at (x, y) and rotated by R(O,180°) what are the coordinates of I’?
(-x , -y)
The equation of all vertical lines takes what form?
x = a
The equation of all horizontal lines takes what form?
y = b
If B is at (7,8) and B’ is at (7,2) what was the axis of reflection?
y = 5
If C is at (-3,2) and C’ is at (11,2) what was the axis of reflection?
x = 4
Given the point A at (5,8), what is the coordinate of A’ if it is translated by T(x,y) = (x-1 , y-2)
(4 , 6)
Given the point A at (5,8), what is the coordinate of A’ if it is dilated by D( O, 1/2 )?
(5/2 , 4)
Given the point A at (5,8), what is the coordinate of A’ if it is reflected about the x axis?
(5 , -8)
Given the point A at (5,8), what is the coordinate of A’ if it is reflected about the y axis?
(-5 , 8)
Given the point A at (5,8), what is the coordinate of A’ if it is rotated by 90º?
(-8 , 5)
Given the point A at (5,8), what is the coordinate of A’ if it is rotated by 180º?
(-5 , -8)
Given the point A at (5,8), what is the coordinate of A’ if it is reflected about the y = 2?
(5 , -4)
Given the point A at (5,8), what is the coordinate of A’ if it is reflected about x = 3?
(1 , 8)
Given the point A at (5,8), what is the coordinate of A’ if it is dilated by D(P , 2) if P is at (1,3)?
(9 , 13)
Describe how you can tell if a figure has rotational (point) symmetry.
If there exists a number of degrees (less than 360º) for which you can rotate the figure around its center and result in an identical figure to the original (in every way).
What are the 3 types of symmetries?
Vertical line symmetry, horizontal line symmetry, and rotational/point symmetry
Describe how you can tell if a figure has vertical line symmetry.
If a vertical line drawn through the center of the figure makes the left and right sides reflections of each other
Describe how you can tell if a figure has horizontal line symmetry.
If a horizontal line drawn through the center of the figure makes the top and bottom reflections of each other.
