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Transformations Flashcards

Translations (69 cards)

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1
Q

What is a translation in geometry?

A

A translation is a function that moves every point of a shape a constant distance in a specified direction.

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2
Q

True or False: A translation changes the shape or size of a figure.

A

False

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3
Q

What are the coordinates of a point after a translation of (3, 4) on point (1, 2)?

A

(4, 6)

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4
Q

Fill in the blank: A translation is defined by a vector that indicates the _____ and _____ of movement.

A

direction, distance

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5
Q

What is the vector notation for a translation moving right 5 units and up 2 units?

A

(5, 2)

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6
Q

If point A is at (2, 3) and is translated by the vector (-1, 4), where is point A’ located?

A

(1, 7)

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7
Q

Multiple Choice: Which of the following is NOT a property of translations?

A

A) It changes the size of the shape

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8
Q

What happens to the orientation of a shape during a translation?

A

The orientation remains the same.

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9
Q

True or False: Translations can be represented using matrices.

A

True

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10
Q

What is the effect of translating a triangle 3 units left and 2 units down?

A

Each vertex of the triangle will move 3 units left and 2 units down.

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11
Q

Fill in the blank: The translation vector is represented as _____ in coordinate notation.

A

(x, y)

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12
Q

What is the result of translating the point (0, 0) by the vector (2, 5)?

A

(2, 5)

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13
Q

Multiple Choice: Which shape maintains its area after a translation?

A

A) All shapes

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14
Q

What is the translation of the rectangle with vertices at (1, 1), (1, 4), (5, 1), and (5, 4) by the vector (2, -3)?

A

The new vertices are (3, -2), (3, 1), (7, -2), and (7, 1).

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15
Q

True or False: Translations can be combined with other transformations like rotations.

A

True

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16
Q

What is the translation of point B from (3, 7) to (8, 9) represented as a vector?

A

(5, 2)

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17
Q

Fill in the blank: Translations can be performed on any _____ in a coordinate plane.

A

geometric figure

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18
Q

What type of transformation is a translation classified as?

A

Rigid transformation

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19
Q

Multiple Choice: Which of the following transformations is NOT rigid?

A

C) Dilation

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20
Q

True or False: A translation can be expressed with the formula (x, y) -> (x + a, y + b).

A

True

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21
Q

What is the resulting position of a square after translating it by the vector (-4, 3)?

A

The square’s vertices will each move 4 units left and 3 units up.

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22
Q

Fill in the blank: The translation vector indicates the _____ and _____ of a translation.

A

magnitude, direction

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23
Q

What is the effect of a translation on the distance between two points?

A

The distance remains unchanged.

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24
Q

Multiple Choice: What is the main characteristic of a translation?

A

B) It preserves distances and angles.

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25
If a shape is translated multiple times, what can be said about the final position?
It is equivalent to a single translation by the sum of all translation vectors.
26
True or False: A translation can be represented on a graph as a straight line.
False
27
What is the image of the point (4, 5) after a translation by the vector (1, -2)?
(5, 3)
28
Fill in the blank: In a translation, the pre-image and image of any point are _____.
equidistant
29
Multiple Choice: Which operation is necessary to determine the new coordinates after a translation?
A) Addition of the translation vector
30
What do you call the original position of a point before translation?
Pre-image
31
True or False: The image of a point after translation is always closer to the origin than the pre-image.
False
32
What is a translation's impact on the symmetry of a shape?
The symmetry is preserved.
33
Fill in the blank: A translation can be described as a _____ transformation.
isometric
34
Multiple Choice: Which of the following shapes can be translated?
C) Circle
35
What is the translation of the point (2, -1) using the vector (-3, 3)?
(-1, 2)
36
True or False: Translations can only occur in one direction.
False
37
What is the geometric effect of translating a line segment?
The line segment maintains its length and slope.
38
Fill in the blank: The result of a translation will always be a shape that is _____ to the original shape.
congruent
39
Multiple Choice: When a shape is translated, what remains unchanged?
B) Size and shape
40
What is the translation vector for moving point (5, 5) to (3, 2)?
(-2, -3)
41
True or False: The translation of a point can be represented as a linear transformation.
True
42
What is the coordinate of point A after translating by vector (0, -4) from point (3, 6)?
(3, 2)
43
Fill in the blank: Translations can be visualized as _____ on a coordinate plane.
slides
44
Multiple Choice: Which of the following is an example of a translation?
A) Moving a triangle 2 units up
45
What remains true about the angles of a shape after a translation?
The angles remain unchanged.
46
True or False: A translation can be represented in vector form.
True
47
What is the image of point (0, 0) after translating by (3, 3)?
(3, 3)
48
Fill in the blank: The translation vector is written as _____.
(a, b)
49
Multiple Choice: Which of the following statements about translations is true?
C) They do not alter the figure's dimensions.
50
What is the relationship between the pre-image and image of a point after translation?
They are separated by the translation vector.
51
True or False: A translation can be performed in a circular path.
False
52
What is the result of translating a square with corners at (1, 1), (1, 2), (2, 1), and (2, 2) by (2, 2)?
(3, 3), (3, 4), (4, 3), (4, 4)
53
Fill in the blank: The translation of a shape does not affect its _____.
position in relation to other shapes
54
Multiple Choice: Which of the following is NOT a characteristic of translations?
A) Changing the shape
55
What vector represents a translation moving a point 6 units left and 4 units down?
(-6, -4)
56
True or False: The result of a translation can be directly calculated using subtraction.
True
57
What is the new position of point (4, 3) after a translation of (-2, 1)?
(2, 4)
58
Fill in the blank: A translation can be represented using a _____ matrix.
transformation
59
Multiple Choice: What does the translation vector (x, y) indicate?
B) The change in coordinates
60
What is the effect of translating a polygon?
The polygon's vertices move according to the translation vector.
61
True or False: A translation can be represented as a function.
True
62
What is the image of the point (2, 3) after translating by (3, -1)?
(5, 2)
63
Fill in the blank: The direction of translation is determined by the _____ of the vector.
orientation
64
Multiple Choice: Which of the following transformations is similar to a translation?
A) Reflection
65
What is the effect of translating a shape in a coordinate plane?
The entire shape moves to a new location without any changes to its form.
66
True or False: Translations can be done in any direction.
True
67
What is the coordinate of point (3, 3) after a translation of (4, 5)?
(7, 8)
68
Fill in the blank: The translation vector consists of two components, _____ and _____.
horizontal, vertical
69
Multiple Choice: Which shape is least affected by a translation?
C) Triangle

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