Translations
Reflections
Rotations
Dilations
Definitions/Postulates
100
What is the formula for doing a translation?
(x, y) → (x + a, y + b)
100
If (a, b) is reflected on the x-axis, what is your new point?
(a, -b)
100
What is the rotation postulate?
A rotation is a rigid motion
100
Is a dilation a rigid motion?
No
100
a transformation in which a figure is enlarged or reduced with respect to a fixed point C called the ___ and a scale factor ___.
center of dilation, k
200
What is A’B’C’ along the vector <4, 4> when triangle ABC has the vertices A(2, -3) B(-6, 7) C(1, 3)?
A'(6, 1) B'(-2, 11) C'(5, 7)
200
What is the line of reflection with of the pre-image B(5, -6) A(7, 4) R(-6, -3) and B’(-5, -6) A’(-7,4) R’(6,-3)?
The y-axis
200
Your points are (3,6) and (8.-4) What is the equation for this rotation if it’s 90 degrees?
(a,b)->(-b,a)
(3,6)-> (-8,-4)
200
If P(x, y) is the pre-image of a point, then its image after a dilation centered at the origin with a scale factor of k P’ is ___.
(kx, ky)
200
What is the difference between a similar figure and a congruent figure?
Similar figures have the same shape but not necessarily the same size whereas
congruent figures are exactly the same.
300
What is the translation postulate?
A translation is a rigid motion.
300
Given the points F(6,6) O(0,0) and R(-4,0), what is the reflection of the triangle FOR over the line y=x?
F′(6,6) O′(0,0) R′(0,-4)
300
What do you have to rotate a point by to create the inverse of the original point.
180 degrees rotated counterclockwise about the origin.
300
Find the scale factor of the dilation from trapezoid P to trapezoid P’ with the center of dilation C.
15/9 or 1 and 2/3
300
What is a glide reflection?
A translation followed by a reflection.
400
The translation (x, y)→(x+a, y+b) maps PQ to P’Q’. Write a rule for the translation of P’Q’ to PQ.
(x-a, y-b)
400
If R(4,1) S(7,3) T(6,4) are the vertices of triangle RST, what will be the vertices of R’T’S’ after the glide reflection of
Translation: (x, y) → (x, y-1)
Rotation: y-axis.
R’(-4, 0) S’(-7, 2) T’(-6, 3)
400
How many times can you rotate this object before it is back where it is started?
8
400
Point C is the center of dilation of the stars. The scale factor is ⅓ . Which figure is the original(pre-image) versus the dilated(image) figure?
The smaller star is the image and the larger star is the pre-image.
400
Which of the transformations are rigid v.s. similar?
Translations, rotations, and reflections are rigid transformations, and dilations are similar.
500
<5, 1> OR (x, y) --> (x+5, y+1)
AND
<-5, -5> OR (x, y) --> (x-5, y-5)
500
The line y=3x+2 is reflected over the line y=-1. What is the equation of the image?
y=-3x-4
500
Rotate the quadrilateral GRAN G(-97.3, 458) R(8274, 0) A(-56.7, 3) N(-93.12, -457) 360° counterclockwise around (27.5, -0.2).
G’(-97.3, 458)
R’(8274, 0)
A’(-56.7, 3)
N’(-93.12, -457)
500
What is the difference between segment as and a’s’ where a(3,2) and s(3,-2) by scale factor ½ with the origin as the center of dilation.
2
500
What are the two components of a vector?
Direction and magnitude!