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

Question 1

A translation moves a figure from one point to another without changing its size or shape. To translate a point (x, y) by 2 units to the right and 1 unit up, which rule should be applied?

Accepted Answer

(x + 2, y + 1)

Answer

(x - 2, y + 1)

Answer

(x + 2, y - 1)

Answer

(x - 2, y - 1)

Question 2

Which transformation is represented by the following rule: (x, y) -> (y, -x)?

Accepted Answer

Reflection

Answer

Translation

Answer

Rotation

Answer

Dilation

Question 3

A rectangle is reflected over the y-axis. Which of the following statements about the resulting figure is true?

Accepted Answer

It is the mirror image of the original.

Answer

It is similar to the original.

Answer

It is congruent to the original.

Answer

It is a completely different shape.

Question 4

A triangle with vertices (1, 2), (3, 4), and (5, 2) is dilated by a scale factor of 2. What are the coordinates of the dilated triangle?

Accepted Answer

(2, 4), (6, 8), (10, 4)

Answer

(0.5, 1), (1.5, 2), (2.5, 1)

Answer

(1, 2), (3, 4), (5, 2)

Question 5

Which of the following describes a composite transformation that results in a rotation followed by a translation?

Accepted Answer

Glide reflection

Answer

Rotation

Answer

Translation

Answer

Dilation

Question 6

A square is translated 3 units to the left, then rotated 180 degrees, and finally reflected over the y-axis. What is the final orientation of the square?

Accepted Answer

Parallel to the original square

Answer

Perpendicular to the original square

Answer

At a 45-degree angle to the original square

Answer

Overlapping the original square

Question 7

If a figure with an area of 12 square units is dilated by a scale factor of 2, the area of the dilated figure will be:

Accepted Answer

24 square units

Answer

6 square units

Answer

12 square units

Answer

48 square units

Question 8

The angle of rotation when a figure is rotated 180 degrees is:

Accepted Answer

180 degrees

Answer

90 degrees

Answer

270 degrees

Answer

360 degrees

Question 9

If a point with coordinates (3, -2) is reflected over the x-axis, its new y-coordinate becomes:

Accepted Answer

2

Answer

-2

Answer

-3

Answer

3

Question 10

A transformation that maps a figure onto itself is called an:

Accepted Answer

Identity transformation

Answer

Translation

Answer

Rotation

Answer

Reflection

Question 11

If a figure with a side length of 8 units is dilated by a scale factor of 0.5, the side length of the dilated figure becomes:

Accepted Answer

4 units

Answer

8 units

Answer

12 units

Answer

16 units

Question 12

A translation of a figure 3 units to the right and 2 units up is represented by the vector:

Accepted Answer

(3, 2)

Answer

(2, 3)

Answer

(-3, -2)

Answer

(-2, -3)

Question 13

What is the image of point (-2, 5) after a rotation of 180 degrees clockwise around the origin?

Accepted Answer

(-2, -5)

Answer

(2, 5)

Answer

(5, -2)

Answer

(-5, 2)

Question 14

A dilation with a scale factor of 0.5 will:

Accepted Answer

Halve the size of the figure

Answer

Double the size of the figure

Answer

Preserve the size of the figure

Answer

Change the shape of the figure

Question 15

What is the center of dilation for a transformation that reduces the size of a rectangle with vertices at (2, 1), (5, 1), (5, 4), and (2, 4) by a scale factor of 0.5?

Accepted Answer

(3, 2.5)

Answer

(2.5, 3)

Answer

(4, 3)

Answer

(3, 4)

Question 16

A composite transformation of a rotation followed by a translation will result in:

Accepted Answer

A glide reflection

Answer

A dilation

Answer

A reflection

Answer

A rotation

Question 17

Which transformation changes the size of a figure?

Accepted Answer

Dilation

Answer

Translation

Answer

Rotation

Answer

Reflection

Question 18

If triangle ABC is translated 5 units to the right, what are the coordinates of its image?

Accepted Answer

A'(x + 5, y), B'(x + 5, y), C'(x + 5, y)

Answer

A'(x, y + 5), B'(x, y + 5), C'(x, y + 5)

Answer

A'(x - 5, y), B'(x - 5, y), C'(x - 5, y)

Answer

A'(x, y - 5), B'(x, y - 5), C'(x, y - 5)

Question 19

What is the ratio of the area of a dilated figure to the original figure if the scale factor is 2?

Accepted Answer

4:1

Answer

1:2

Answer

2:1

Answer

1:4

Question 20

Which transformation preserves the figure's orientation?

Accepted Answer

Rotation

Answer

Reflection

Answer

Translation

Answer

Dilation

Question 21

What are the coordinates of the image of point P(x, y) after a reflection across the line y = x?

Accepted Answer

(y, x)

Answer

(x, y)

Answer

(-x, y)

Answer

(-y, x)

Question 22

Which composite transformation is equivalent to a 180-degree rotation?

Accepted Answer

Reflection across the x-axis followed by reflection across the y-axis

Answer

Reflection across two perpendicular lines

Answer

Translation followed by dilation

Answer

Rotation followed by translation

Question 23

Which of the following describes a reflection along the y-axis?

Accepted Answer

Flips the figure across a vertical line

Answer

Flips the figure across a horizontal line

Answer

Enlarges or reduces the figure

Answer

Moves the figure without changing its size or shape

Question 24

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

Accepted Answer

2

Answer

0.5

Answer

1

Answer

4

Question 25

Which transformation preserves distance between points?

Accepted Answer

Translation

Answer

Rotation

Answer

Reflection

Answer

Dilation

Question 26

What is the image of point (-3, 2) after a reflection along the x-axis?

Accepted Answer

(-3, -2)

Answer

(3, 2)

Answer

(3, -2)

Answer

(-3, 2)

Question 27

Which type of transformation is created by performing a translation followed by a rotation?

Accepted Answer

Composite

Answer

Translation

Answer

Rotation

Answer

Reflection

Question 28

When performing composite transformations, which transformation is applied first?

Accepted Answer

The first transformation listed

Answer

The last transformation listed

Answer

Both transformations are applied simultaneously

Answer

The order does not matter

Question 29

Which of the following is NOT a transformation that can be applied to a geometric figure?

Accepted Answer

Addition

Answer

Translation

Answer

Rotation

Answer

Reflection

Question 30

Which transformation is represented by the rule: (x, y) -> (x + 3, y - 2)?

Accepted Answer

Translation

Answer

Rotation

Answer

Reflection

Answer

Dilation

Question 31

Which of the following describes the properties of a dilation transformation?

Accepted Answer

Preserves shape and orientation; increases distances by a constant factor.

Answer

Flips the figure over a line; preserves distances.

Answer

Increases distances by a constant factor; changes the figure's orientation.

Answer

Preserves shape and orientation; flips the figure over a line.

Question 32

A translation is characterized by:

Accepted Answer

Moving a figure without changing its orientation

Answer

Increasing or decreasing the figure's size

Answer

Changing the figure's shape

Answer

Rotating the figure around a fixed point

Question 33

Which transformation involves flipping a figure across a line?

Accepted Answer

Reflection

Answer

Translation

Answer

Rotation

Answer

Dilation

Question 34

Which of the following is NOT a characteristic of dilation?

Accepted Answer

Changing the figure's shape

Answer

Enlarging or reducing the figure

Answer

Stretching or shrinking the figure

Answer

Preserving the figure's angles

Question 35

A composite transformation is a sequence of:

Accepted Answer

Any combination of transformations

Answer

Only translations

Answer

Only rotations

Answer

Only reflections

Question 36

What is the inverse transformation of a translation to the right?

Accepted Answer

Translation to the left

Answer

Rotation 180 degrees

Answer

Reflection across the y-axis

Answer

Dilation with a scale factor of 1

Question 37

If a figure is rotated 270 degrees counterclockwise around the origin, how will its coordinates change?

Accepted Answer

They will change sign and quadrant

Answer

They will only change sign

Answer

They will only change quadrant

Answer

They will not change

Question 38

Which transformation can enlarge a figure without changing its shape?

Accepted Answer

Dilation

Answer

Translation

Answer

Rotation

Answer

Reflection

Question 39

A reflection across the y-axis is also known as:

Accepted Answer

Vertical reflection

Answer

Horizontal reflection

Answer

Diagonal reflection

Answer

Parallel reflection

Question 40

Which transformation alters the size of a geometric figure?

Accepted Answer

Dilation

Answer

Translation

Answer

Rotation

Answer

Reflection

Question 41

A segment with endpoints (2, 3) and (6, 7) undergoes a translation of 4 units to the right. What are the coordinates of the new endpoints?

Accepted Answer

(8, 9) and (12, 13)

Answer

(6, 7) and (10, 11)

Answer

(10, 11) and (14, 15)

Answer

(12, 13) and (16, 17)

Question 42

Which transformation increases the area of a figure?

Accepted Answer

Dilation

Answer

Translation

Answer

Rotation

Answer

Reflection

Question 43

A rectangle of length 10 cm and width 5 cm undergoes a dilation with a scale factor of 2. What are the new dimensions?

Accepted Answer

Length: 20 cm, Width: 5 cm

Answer

Length: 5 cm, Width: 2.5 cm

Answer

Length: 10 cm, Width: 5 cm

Answer

Length: 10 cm, Width: 10 cm

Question 44

Which transformation is not considered a rigid transformation?

Accepted Answer

Dilation

Answer

Translation

Answer

Rotation

Answer

Reflection

Question 45

A figure undergoes a translation of 3 units to the right and 2 units down. What is its inverse transformation?

Accepted Answer

Translation 3 units to the left and 2 units up

Answer

Translation 2 units to the right and 3 units down

Answer

Translation 3 units to the left and 2 units down

Answer

Translation 2 units to the right and 3 units up

Question 46

A trapezoid with vertices A(0, 0), B(4, 0), C(6, 4), and D(2, 4) undergoes a dilation with a scale factor of 1/2. What are the coordinates of its new vertices?

Accepted Answer

A'(0, 0), B'(2, 0), C'(3, 2), D'(1, 2)

Answer

A'(1, 1), B'(2, 2), C'(3, 3), D'(1, 3)

Answer

A'(0, 0), B'(4, 0), C'(6, 4), D'(2, 4)

Answer

A'(2, 2), B'(4, 4), C'(6, 6), D'(4, 6)

Question 47

Which transformation moves a figure from one position to another without changing its size or shape?

Accepted Answer

Translation

Answer

Reflection

Answer

Dilation

Answer

Rotation

Question 48

Which transformation creates an image of a figure that is a mirror image across a line?

Accepted Answer

Reflection

Answer

Translation

Answer

Dilation

Answer

Rotation

Question 49

A figure is enlarged by a dilation with a scale factor of 2. What is the effect of a dilation with a scale factor of 0.5 on the same figure?

Accepted Answer

Reduces the figure to half its original size

Answer

Rotates the figure 180 degrees

Answer

Enlarges the figure to twice its original size

Question 50

A triangle has coordinates (2, 4). After being translated 3 units to the right and 2 units up, what are the coordinates of the translated triangle?

Accepted Answer

(5, 6)

Answer

(2, 6)

Answer

(5, 4)

Answer

(3, 6)

Question 51

A line with equation y = 2x + 1 is reflected over the y-axis. What is the equation of the transformed line?

Accepted Answer

y = -2x + 1

Answer

y = 2x - 1

Answer

y = x + 1

Answer

y = -x + 1

Question 52

A circle is dilated with a scale factor of 3. What is the ratio of the area of the transformed circle to the original circle?

Accepted Answer

9:1

Answer

3:1

Answer

1:9

Answer

1:3