Master Geometric Transformations: Translations, Rotations, Reflections, and Dilations

Question 1

Which transformation results in a figure that is a mirror image of the original figure across a line?

Accepted Answer

Reflection

Answer

Translation

Answer

Rotation

Answer

Dilation

Question 2

What is the scale factor if a figure is dilated by a factor of 2?

Accepted Answer

2

Answer

0.5

Answer

1

Answer

4

Question 3

Which of the following is NOT a rigid transformation?

Accepted Answer

Dilation

Answer

Translation

Answer

Rotation

Answer

Reflection

Question 4

If a figure is translated by the vector <3, -4>, what is the new position of the point (1, 2)?

Accepted Answer

(4, -2)

Answer

(1, -2)

Answer

(4, 2)

Answer

(1, 6)

Question 5

What is the center of dilation for a figure that is dilated by a scale factor of 0.5 and has a new vertex at (2, 3) if the original vertex was at (4, 6)?

Accepted Answer

(1, 1.5)

Answer

(2, 3)

Answer

(4, 6)

Answer

(0, 0)

Question 6

What is the equation of the line of reflection for a figure that has been reflected across the y-axis?

Accepted Answer

x = 0

Answer

y = 0

Answer

y = x

Answer

x = y

Question 7

Which of the following is NOT a type of rigid geometric transformation?

Accepted Answer

Scaling

Answer

Translation

Answer

Rotation

Answer

Reflection

Question 8

When a figure is reflected across the y-axis, what happens to its x-coordinate?

Accepted Answer

Changes sign

Answer

Remains the same

Answer

Is multiplied by -1

Answer

Is divided by -1

Question 9

A dilation with a scale factor of 2 is applied to a figure. What is the ratio of the new figure's area to the original figure's area?

Accepted Answer

4

Answer

1/2

Answer

1

Answer

2

Question 10

After a figure is rotated 180 degrees around a fixed point, which property remains unchanged?

Accepted Answer

Shape of the figure

Answer

Distance between points

Answer

Orientation of the figure

Answer

Area of the figure

Question 11

What is the order of transformations in the following composite transformation: reflection across the x-axis followed by a translation 5 units up?

Accepted Answer

Reflection(x-axis) followed by Translation(0, 5)

Answer

Translation(0, 5) followed by Reflection(x-axis)

Answer

Translation(5, 0) followed by Reflection(y-axis)

Answer

Reflection(y-axis) followed by Translation(5, 0)

Question 12

What is the equation for a reflection over the x-axis?

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 13

What is the scale factor for a dilation that triples the area of a figure?

Accepted Answer

9

Answer

1

Answer

3

Answer

12

Question 14

What is the equation for a translation of 3 units to the left and 4 units down?

Accepted Answer

(x, y) -> (x - 3, y - 4)

Answer

(x, y) -> (x + 3, y - 4)

Answer

(x, y) -> (x - 3, y + 4)

Answer

(x, y) -> (x + 3, y + 4)

Question 15

Which property is NOT characteristic of a rigid transformation?

Accepted Answer

Preserves area

Answer

Preserves distance

Answer

Preserves shape

Answer

Preserves orientation

Question 16

Which of the following is NOT a rigid transformation?

Accepted Answer

Dilation

Answer

Reflection

Answer

Rotation

Answer

Translation

Question 17

A composite transformation consists of a rotation followed by a reflection. Which of the following is NOT a characteristic of a composite transformation?

Accepted Answer

The composite transformation is always a rigid transformation.

Answer

The order of transformations matters.

Answer

The overall transformation is a combination of both individual transformations.

Answer

The result depends on the specific transformations used.

Question 18

A figure is translated 3 units to the left and then reflected over the x-axis. Which transformation is equivalent to this composite transformation?

Accepted Answer

Reflection over the y-axis

Answer

Translation 3 units to the right

Answer

Rotation 180 degrees about the origin

Answer

Dilation with a scale factor of 1/2

Question 19

A point (x, y) is transformed by a dilation with a scale factor of 3 and then by a translation 2 units to the right. Which of the following represents the coordinates of the final image point?

Accepted Answer

(3x + 2, 3y)

Answer

(3x, 3y + 2)

Answer

(3x + 2, y)

Answer

(x + 2, 3y)

Question 20

Which transformation preserves the shape of a figure but changes its size?

Accepted Answer

Dilation

Answer

Translation

Answer

Rotation

Answer

Reflection

Question 21

A translation is represented by the vector (a, b). What is the translation when the vector is multiplied by 2?

Accepted Answer

(2a, 2b)

Answer

(3a, 3b)

Answer

(a, a)

Answer

(a/2, b/2)

Question 22

A polygon undergoes a dilation with a scale factor of 0.5. What is the ratio of the area of the dilated polygon to the original polygon?

Accepted Answer

1:4

Answer

2:1

Answer

4:1

Answer

1:2

Question 23

A figure is rotated 90 degrees clockwise and then translated 5 units to the right. What is the resulting transformation?

Accepted Answer

Rotation of 90 degrees clockwise followed by translation of 5 units to the right

Answer

Dilation with a scale factor of 1

Answer

Translation of 5 units to the right followed by rotation of 90 degrees clockwise

Answer

Reflection across the y-axis

Question 24

Which transformation flips a figure over a line?

Accepted Answer

Reflection

Answer

Rotation

Answer

Translation

Question 25

Which sequence of transformations maps a triangle onto itself?

Accepted Answer

Reflection over the x-axis followed by a rotation by 180 degrees around the origin

Answer

Dilation by a factor of 2 followed by a reflection over the y-axis

Answer

Rotation by 90 degrees around the origin followed by a translation by the vector (3, 5)

Question 26

Identify the transformation that maps a figure onto itself without changing its size or shape.

Accepted Answer

Identity transformation

Answer

Reflection

Answer

Rotation

Answer

Translation

Question 27

A translation transformation:

Accepted Answer

Moves a figure without altering its size or shape

Answer

Reflects a figure across a designated line

Answer

Rotates a figure around a specified point

Question 28

A reflection transformation flips a figure:

Accepted Answer

Over a specified line

Answer

Around a fixed point

Answer

Along a specified vector

Answer

Onto itself

Question 29

A rotation transformation involves:

Accepted Answer

Turning a figure around a fixed point

Answer

Moving a figure along a line

Answer

Enlarging or reducing a figure

Answer

Reflecting a figure over a line

Question 30

A dilation transformation:

Accepted Answer

Enlarges or reduces a figure by a specified factor

Answer

Reflects a figure across a designated line

Answer

Rotates a figure around a fixed point

Answer

Moves a figure without changing its size or shape

Question 31

A sequence of two reflections over parallel lines is equivalent to:

Accepted Answer

A translation

Answer

A rotation

Answer

A reflection

Question 32

A transformation that maps a figure onto a line is termed:

Accepted Answer

Projection

Answer

Translation

Answer

Dilation

Answer

Reflection

Question 33

If a point (2, 3) is rotated 90 degrees counterclockwise about the origin, what are the coordinates of its image?

Accepted Answer

(-3, 2)

Answer

(2, -3)

Answer

(-2, -3)

Answer

(3, -2)

Question 34

A dilation with a scale factor of 2 centered at the origin is applied to the point (3, 4). What are the coordinates of the image?

Accepted Answer

(6, 8)

Answer

(-6, -8)

Answer

(3, 2)

Answer

(2, 4)

Question 35

A figure is reflected across the x-axis and then shifted 3 units to the right. What is the resulting transformation?

Accepted Answer

Reflection followed by translation

Answer

Translation followed by reflection

Answer

Dilation followed by translation

Answer

Rotation followed by reflection

Question 36

Which transformation will result in the most significant change in the size and shape of a figure?

Accepted Answer

Dilation with a scale factor less than 1

Answer

Translation

Answer

Reflection

Answer

Rotation

Question 37

A figure is dilated by a factor of 1.5 and then reflected across the y-axis. Which describes the resulting transformation?

Accepted Answer

Dilation followed by reflection

Answer

Reflection followed by dilation

Answer

Rotation followed by dilation

Answer

Translation followed by reflection

Question 38

Which transformation moves every point of a figure the same distance in the same direction?

Accepted Answer

Translation

Answer

Rotation

Answer

Dilation

Answer

Reflection

Question 39

A triangle is reflected across the y-axis. What is always true about the image and pre-image?

Accepted Answer

They are congruent.

Answer

The orientation remains the same.

Answer

The image is smaller.

Answer

The image is larger.

Question 40

What are the coordinates of the image of point (2, 3) after a 90-degree counterclockwise rotation about the origin?

Accepted Answer

(-3, 2)

Answer

(3, -2)

Answer

(2, -3)

Answer

(-2, -3)

Question 41

A rectangle is dilated by a scale factor of 3. How does the area of the image compare to the area of the original rectangle?

Accepted Answer

The image's area is 9 times the original rectangle's area.

Answer

The image's area is one-third of the original rectangle's area.

Answer

The image's area is 3 times the original rectangle's area.

Question 42

Which transformation does NOT preserve the orientation of a figure?

Accepted Answer

Reflection

Answer

Rotation

Answer

Dilation

Answer

Translation

Question 43

A figure is transformed by a translation of 3 units to the right and 2 units down, followed by a reflection across the x-axis. What single transformation is equivalent to this sequence?

Accepted Answer

Reflection across the line y = -2 followed by a translation 3 units to the right

Answer

Reflection across the line y = 2 followed by a translation 3 units to the right

Answer

Translation 3 units to the right followed by a reflection across the line y = 2

Question 44

A point is located at (4, -5). What will be the y-coordinate of its image after a reflection across the line y = x?

Accepted Answer

4

Answer

5

Answer

-5

Answer

-4

Question 45

A triangle undergoes a dilation with a scale factor of 1/2. Which statement best describes the relationship between the angles of the pre-image and the image?

Accepted Answer

The corresponding angles are congruent.

Answer

The corresponding angles are supplementary.

Answer

The angles of the image are half the measure of the angles of the pre-image.

Question 46

What is the image of the point (-5, 7) after a translation 2 units to the left and 4 units up?

Accepted Answer

(-7, 11)

Answer

(-3, 3)

Answer

(-3, 11)

Answer

(-7, 3)

Question 47

A square is rotated 180 degrees about its center. Which of the following statements is NOT true?

Accepted Answer

The image is in a different location than the pre-image.

Answer

All four vertices of the square map onto themselves.

Answer

The image and pre-image are congruent.

Question 48

Which of the following transformations preserves the shape and size of a figure?

Accepted Answer

Rotation

Answer

Reflection

Answer

Dilation

Answer

Translation

Question 49

A translation moves a figure by a given distance in a given direction. What is the correct notation for a translation?

Accepted Answer

(x, y) -> (x + a, y + b)

Answer

(x, y) -> (x, y + b)

Answer

(x, y) -> (x + a, y)

Question 50

What is the center of rotation for a figure that has been rotated 180 degrees?

Accepted Answer

The midpoint of the line segment connecting the pre-image and image

Answer

The origin of the coordinate plane

Answer

The centroid of the figure

Question 51

A reflection flips a figure over a line. What is the name of the line over which the reflection occurs?

Accepted Answer

Line of reflection

Answer

Axis of rotation

Answer

Center of dilation

Answer

Translation vector

Question 52

Which of the following transformations results in a figure that is similar to the original figure?

Accepted Answer

Dilation

Answer

Translation

Answer

Reflection

Answer

Rotation

Question 53

A dilation increases or decreases the size of a figure by a certain factor. What is the name of this factor?

Accepted Answer

Scale factor

Answer

Rotation angle

Answer

Reflection ratio

Answer

Translation distance

Question 54

Which of the following is NOT a rigid transformation?

Accepted Answer

Dilation

Answer

Rotation

Answer

Translation

Answer

Reflection

Question 55

A figure is rotated 90 degrees clockwise around the point (2, 3). What are the coordinates of the image of the point (5, 7)?

Accepted Answer

(7, 2)

Answer

(5, 2)

Answer

(2, 7)

Answer

(3, 5)

Question 56

A figure is reflected over the y-axis. What is the effect of this transformation on the x-coordinate of a point?

Accepted Answer

It changes sign.

Answer

It is multiplied by 2.

Answer

It stays the same.

Question 57

A figure is dilated by a scale factor of 2. What is the effect of this transformation on the area of the figure?

Accepted Answer

It is multiplied by 4.

Answer

It is multiplied by 2.

Answer

It is divided by 2.

Answer

It stays the same.