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Geometry > Transformations: Rorations > Flashcards

Transformations: Rorations Flashcards

0
Q

Pre-image

A

A figure that is about undergo a transformation

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1
Q

Transformation

A

A function that moves something along a coordinate plane

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2
Q

Image

A

A figure that has undergone my transformation

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3
Q

Distance Preserving

A

The distance between the image of the two points is always equal to the distance between the pre-image of the two points

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4
Q

Angle preserving

A

The angle measure of the image is equal to the angle measure of the pre-image

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5
Q

What do you need to perform a rigid motion rotation?

A

The center of rotation and direction

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6
Q

Rotational Symmetry

A

If a figure is it’s own image under a center of rotation and the center of the rotation is the only fixed point

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7
Q

Order of Rotational Symmetry

A

The number of degrees a figure must be rotated in order to see an identical image

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8
Q

Positive rotations

A

Counter-clockwise

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9
Q

Negative Rotations

A

Clockwise

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10
Q

How do u name the equivalent rotation?

A

Subtract the # by 360

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11
Q

Rotation of 180 degrees

A

P(x,y)–p’(-x,-y)

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12
Q

Rotation of 90 degrees

A

P(x,y)–p’(-y,x)

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13
Q

Rotation of -90 degrees

A

P(x,y)–p’(y,-x)

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14
Q

Rotation of 360 degrees

A

P(x,y)–p’(x,y) (orientation is maintained)

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15
Q

Rotation of 270 degrees

A

P(x,y)–p’(y,-x)

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16
Q

After a rotation, point P= P’

A

Point P and point P’ were two distinct points located on the same arc of rotation
Point P and point P’ were two distinct points equidistant from the center of rotation

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17
Q

Rotation over the y axis (ry-axis)

A

P(x,y)–P’(-x,y)

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18
Q

Rotation over the x axis (rx-axis)

A

P(x,y)–P’(x,-y)

19
Q

Reflection over the line y=x

A

P(x,y)–P’(y,x)

20
Q

Reflection in the line y=-x

A

P(x,y)–P’(-y,-x)

21
Q

Basic Rigid Motion (Isometry)

A

A transformation that preserves lengths of two segments and measures of angles

22
Q

Rigid motion

A

Performing a transformation that didn’t change the size/ angle measure

23
Q

R o=

A

R 180

24
Q

Name the order of rotational symmetry for regular polygons

A

360/N (# of sides)

25
Q

Point symmetry

A

180 degrees

26
Q

State the properties in which dilation

is altered

A

K1 ~ get larger

27
Q 
Which is not an Isometry? 
Line reflection
Dilation
Point reflection
Translation
A

Dilation

28
Q 
Which property isn't preserved under ry=x?
Distance
Angle measure
Orientation 
Parallelism
A

Orientation

29
Q

Which transformation is a direct Isometry?

A

(x,y)-(-x,-y)
And
(x,y)-(x-5,y-2)

30
Q 
Which transformation does not preserve orientation?
(x,y)-(-x,-y)
(x,y)-(x+3,y+2)
(x,y)-(2x,2y)
(x,y)-(y,x)
A

(x,y)-(y,x)

31
Q 
Which transformation is an example of a direct Isometry?
rx,
R40,
D-3,
ry=5
A

R40

32
Q 
Which transformation is an opposite Isometry?
R-90
T3,-4
D-2
rx=1
A

rx=1

33
Q

If KL=8 and K’L’=12, then the constant of dilation is ___ an the dilation is a (an) ____

A

12/8=3/2

3/2, enlargement

34
Q

Point reflections preserve

A

Distance, angle measure, and orientation

35
Q

Find the image under the same dilation

A

K= ending/beginning

36
Q

Find 3 transformations with the same output

A

R0, R180, D-1

-x,-y

37
Q

Opposite isometries

A

Line reflections and glide reflections

38
Q

Direct isometries

A

Point reflections, rotations, and translations

Preserve orientation

39
Q

Composition

A

The output of one transformation is the input of another transformation. Work from right to left

40
Q

Dilation

A

Increasing size, perimeter changes, orientation is invariant

41
Q

Find D2 ° D1/2 of (x,y)

A

Inverse (x,y) - (x,y)

It stays the same

42
Q

If line a is parallel to line b, then ra ° rb (^ CTH) is equivalent to a

A

Translation

43
Q

ry=x ° rx produces a transformation that is

A

A direct Isometry

44
Q

When u dilate a pre-image the image’s angles are in a

A

1:1 ratio

45
Q 
What transformation doesn't preserve orientation?
(x,y)-(-y,x)
(x,y)-(-y,-x)
(x,y)-(y+3,x)
(x,y)-(-3y,-3x)
A

(x,y)-(-y,-x)

Geometry (6 decks)

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