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

Question 1

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

Accepted Answer

Translation 3 units left, 2 units up

Answer

Translation 3 units right, 2 units down

Answer

Rotation 90 degrees clockwise

Answer

Reflection over the y-axis

Question 2

If a point (x, y) is translated 5 units to the right, what are the new coordinates of the point?

Accepted Answer

(x + 5, y)

Answer

(x, y + 5)

Answer

(x - 5, y)

Answer

(x, y - 5)

Question 3

Which of the following transformations preserves both distance and angle measure?

Accepted Answer

Translation

Answer

Rotation

Answer

Reflection

Answer

Dilation

Question 4

If a figure is reflected over the x-axis and then rotated 180 degrees about the origin, what is the overall transformation?

Accepted Answer

Reflection

Answer

Translation

Answer

Rotation

Answer

Dilation

Question 5

What is the scale factor of a dilation that makes a figure twice as large?

Accepted Answer

2

Answer

0.5

Answer

1

Answer

4

Question 6

A translation is a transformation that moves a figure:

Accepted Answer

Parallel to a line, without changing its size or shape

Answer

Perpendicular to a line, without changing its size or shape

Answer

Along a circle, without changing its size or shape

Answer

Around a point, without changing its size or shape

Question 7

A dilation with a scale factor of 2 will:

Accepted Answer

Double the size of the figure

Answer

Halve the size of the figure

Answer

Increase the size of the figure by 50%

Answer

Decrease the size of the figure by 50%

Question 8

A figure is rotated 90 degrees counterclockwise around the origin. Which of the following is NOT true about the resulting figure?

Accepted Answer

The perimeter of the figure changes

Answer

The x-coordinates of the vertices change sign

Answer

The y-coordinates of the vertices change sign

Answer

The area of the figure remains the same

Question 9

Which of the following transformations is NOT an isometry?

Accepted Answer

Dilation

Answer

Translation

Answer

Rotation

Answer

Reflection

Question 10

Translate the point (x, y) by 3 units to the right and 2 units up. What is the rule?

Accepted Answer

(x + 3, y + 2)

Answer

(x - 3, y - 2)

Answer

(x + 2, y + 3)

Answer

(x - 2, y - 3)

Question 11

Which is NOT a characteristic of a dilation?

Accepted Answer

Moves the figure

Answer

Preserves shape

Answer

Changes size

Answer

Has a fixed point

Question 12

Which transformation is NOT a rigid transformation?

Accepted Answer

Dilation

Answer

Translation

Answer

Rotation

Answer

Reflection

Question 13

Which sequence of transformations will result in a figure rotated 180 degrees?

Accepted Answer

Reflection over the x-axis followed by a reflection over the y-axis

Answer

Rotation of 90 degrees clockwise followed by a rotation of 90 degrees counterclockwise

Answer

Dilation by a scale factor of -1 followed by a translation

Answer

Translation followed by a reflection over the line y = x

Question 14

In geometric transformations, which type of transformation involves moving a figure from one point to another without changing its size or shape?

Accepted Answer

Translation

Answer

Rotation

Answer

Reflection

Answer

Dilation

Question 15

What is the effect of a dilation with a scale factor of 2?

Accepted Answer

Doubles the size of the figure

Answer

Halves the size of the figure

Answer

Enlarges the figure by 200%

Answer

Reduces the figure by 50%

Question 16

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

Accepted Answer

Reflection

Answer

Translation

Answer

Rotation

Answer

Dilation

Question 17

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

Accepted Answer

2

Answer

0.5

Answer

1

Answer

4

Question 18

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

Accepted Answer

Scale

Answer

Reflection

Answer

Rotation

Answer

Translation

Question 19

A dilation changes the size of a figure. What is the dilation factor for the transformation (x, y) → (2x, 2y)?

Accepted Answer

2

Answer

3

Answer

4

Answer

0.5

Question 20

A transformation consists of the following sequence: translation 3 units right, rotation 90 degrees counterclockwise about the origin, and another translation 5 units down. What is the overall effect of this composite transformation?

Accepted Answer

Figure is translated 3 units right, rotated 90 degrees counterclockwise, and then translated 5 units down

Answer

Figure is flipped over the y-axis, rotated 90 degrees counterclockwise, and then translated 3 units left

Answer

Figure is translated 5 units down, rotated 90 degrees clockwise, and then translated 3 units left

Question 21

Which of the following transformations preserves both distance and angle measure?

Accepted Answer

Translation

Answer

Dilation

Answer

Rotation

Answer

Reflection

Question 22

Which of the following statements does NOT describe a reflection transformation?

Accepted Answer

Preserves orientation

Answer

Flips a figure over a line

Answer

Creates a mirror image

Question 23

A line segment with endpoints (1, 2) and (3, 4) is dilated by a scale factor of 3 with respect to the origin. What are the coordinates of the dilated line segment?

Accepted Answer

(3, 6), (9, 12)

Answer

(1, 3), (3, 6)

Answer

(2, 3), (4, 6)

Answer

(1, 2), (3, 4)

Question 24

Which of the following sequences of transformations will map a square onto a rhombus?

Accepted Answer

Dilation, rotation

Answer

Dilation, translation, reflection

Answer

Rotation, dilation, reflection

Answer

Reflection, translation, rotation

Question 25

A rectangle with vertices (0, 0), (3, 0), (3, 2), and (0, 2) is reflected over the y-axis and then rotated 180 degrees around the origin. What is the resulting shape?

Accepted Answer

Rectangle

Answer

Trapezoid

Answer

Triangle

Answer

Square

Question 26

Which of the following is NOT a rigid transformation?

Accepted Answer

Dilation

Answer

Translation

Answer

Rotation

Answer

Reflection

Question 27

A triangle with vertices (2, 1), (4, 3), and (6, 1) is translated 3 units to the right and 2 units up. What are the coordinates of the translated triangle?

Accepted Answer

(5, 3), (7, 5), (9, 3)

Answer

(2, 3), (4, 5), (6, 3)

Answer

(5, 1), (7, 3), (9, 1)

Answer

(2, 1), (4, 3), (6, 1)

Question 28

Which of the following is the inverse transformation of a rotation 60 degrees counterclockwise?

Accepted Answer

Rotation 60 degrees clockwise

Answer

Translation 2 units to the left

Answer

Reflection over the y-axis

Answer

Dilation by a scale factor of 3

Question 29

After translating a figure (5, -2) units to the right and 3 units down, what are its new coordinates?

Accepted Answer

(10, -5)

Answer

(5, 3)

Answer

(0, -5)

Question 30

Which transformation creates a mirror image across a line?

Accepted Answer

Reflection

Answer

Rotation

Answer

Translation

Answer

Dilation

Question 31

In a dilation, what value represents the factor by which the original figure is increased or decreased?

Accepted Answer

Scale factor

Answer

Translation distance

Answer

Rotation angle

Answer

Reflection line

Question 32

Which transformation will result in a larger image?

Accepted Answer

Dilation with a scale factor greater than 1

Answer

Dilation with a scale factor less than 1

Answer

Reflection

Answer

Translation

Question 33

A transformation moves a point 3 units to the left and 5 units down. What is the translation vector for this transformation?

Accepted Answer

(-3, -5)

Answer

(-3, 5)

Answer

(3, -5)

Answer

(3, 5)

Question 34

Which transformation flips a figure over a line?

Accepted Answer

Reflection

Answer

Rotation

Answer

Dilation

Answer

Translation

Question 35

A trapezoid is reflected over the line y = x. If point T has coordinates (3, -5), what are the coordinates of its image, T'?

Accepted Answer

(-5, 3)

Answer

(3, 5)

Answer

(5, 3)

Answer

(-5, -3)

Question 36

Which transformation preserves both shape and size of a figure?

Accepted Answer

Isometry

Answer

Dilation

Answer

Translation

Answer

Rotation

Question 37

A triangle with vertices at (1, 2), (3, 4), and (5, 2) is reflected across the y-axis. What are the coordinates of the image?

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 38

A quadrilateral is translated 3 units to the right and 2 units down. If one of the vertices of the original quadrilateral is at (2, 5), what is the corresponding vertex in the image?

Accepted Answer

(5, 3)

Answer

(5, 7)

Answer

(-1, 3)

Question 39

A square is rotated 90 degrees clockwise about its center. Which of the following describes the orientation of the image compared to the original square?

Accepted Answer

Rotated 90 degrees clockwise

Answer

Reflected across a vertical line

Answer

Reflected across a horizontal line

Answer

Rotated 180 degrees

Question 40

A circle with a radius of 5 units is dilated by a scale factor of 2. What is the radius of the image?

Accepted Answer

10 units

Answer

5 units

Answer

15 units

Answer

2.5 units

Question 41

A triangle is transformed by a combination of a translation, a reflection, and a rotation. Which of the following is true about the image?

Accepted Answer

The image is congruent to the original triangle.

Answer

The image is larger than the original triangle.

Answer

The image is smaller than the original triangle.

Answer

The image is similar to the original triangle.

Question 42

Which transformation can be used to create a tessellation?

Accepted Answer

Translation

Answer

Dilation

Answer

Rotation

Answer

Reflection

Question 43

A regular hexagon is rotated about its center. What is the smallest angle of rotation that will map the hexagon onto itself?

Accepted Answer

60 degrees

Answer

90 degrees

Answer

30 degrees

Answer

120 degrees

Question 44

A rectangle is reflected across a horizontal line. What is the orientation of the image compared to the original rectangle?

Accepted Answer

Flipped vertically

Answer

Flipped horizontally

Answer

Rotated 180 degrees

Answer

Rotated 90 degrees

Question 45

A triangle is dilated by a scale factor of 1/2. What is the effect of this dilation on the area of the triangle?

Accepted Answer

The area is reduced to 1/4 of the original area.

Answer

The area is reduced to 1/2 of the original area.

Answer

The area remains the same.

Answer

The area is doubled.