Geometry Transformations: Master the Art of Moving Shapes

Question 1

Which transformation changes the size or shape of a figure?

Accepted Answer

C. Dilation

Answer

A. Rotation

Answer

B. Translation

Answer

D. Reflection

Question 2

A figure undergoes a translation on the coordinate plane. It moves 5 units to the right and 3 units up. Write the correct notation for this transformation.

Accepted Answer

Translation: (5, 3)

Answer

Reflection: y-axis

Answer

Rotation: 90 degrees clockwise

Answer

Dilation: scale factor of 2

Question 3

Which transformation changes the distance between points in a figure?

Accepted Answer

Dilation

Answer

Translation

Answer

Reflection

Answer

Rotation

Question 4

Which of the following transformations is non-rigid?

Accepted Answer

Enlargement

Answer

Translation

Answer

Reflection

Answer

Rotation

Question 5

Which of the following transformations is NOT a rigid motion?

Accepted Answer

Dilation

Answer

Translation

Answer

Rotation

Answer

Reflection

Question 6

Which operation modifies the size of a figure rather than transforming it?

Accepted Answer

Dilation

Answer

Translation

Answer

Reflection

Answer

Rotation

Question 7

Which transformation can alter the size of a figure?

Accepted Answer

Dilation

Answer

Translation

Answer

Rotation

Answer

Reflection

Question 8

A figure was moved 5 units to the left and 3 units up. Which transformation was performed?

Accepted Answer

Translation

Answer

Rotation

Answer

Reflection

Answer

Dilation

Question 9

Which transformation maps point P(2, 3) to point Q(4, 7)?

Accepted Answer

Translation: (x, y) -> (x + 2, y + 4)

Answer

Reflection across the x-axis: (x, y) -> (x, -y)

Answer

Rotation 90 degrees counterclockwise: (x, y) -> (y, -x)

Answer

Dilation by a factor of 2: (x, y) -> (2x, 2y)

Question 10

Which transformation can multiply the area of a quadrilateral by 4?

Accepted Answer

Dilation

Answer

Translation

Answer

Reflection

Answer

Rotation

Question 11

Which transformation alters the size and/or shape of a figure?

Accepted Answer

Dilation

Answer

Translation

Answer

Reflection

Answer

Rotation

Question 12

In a coordinate plane, which transformation will create an image that is identical in shape and size to the original figure but appears reversed?

Accepted Answer

Reflection

Answer

Translation

Answer

Rotation

Question 13

Which transformation changes the size of a figure?

Accepted Answer

Dilation

Answer

Translation

Answer

Rotation

Question 14

To translate a point (x,y) 5 units right and 2 units down, which transformation should be applied?

Accepted Answer

Translation: (x+5, y-2)

Answer

Reflection: (x+5, -y-2)

Answer

Rotation: (-x-5, y+2)

Answer

Dilation: (2x+5, 2y-2)

Question 15

Which matrix represents a 90-degree counterclockwise rotation around the origin?

Accepted Answer

[0 -1; 1 0]

Answer

[-1 0; 0 1]

Answer

[0 1; -1 0]

Answer

[1 0; 0 -1]

Question 16

Which transformation requires the identification of a specific point around which the figure pivots?

Accepted Answer

Rotation

Answer

Translation

Answer

Reflection

Answer

Dilation

Question 17

Which transformation creates a figure that is similar but not congruent to the original figure?

Accepted Answer

Dilation

Answer

Translation

Answer

Rotation

Answer

Reflection

Question 18

A circle with a radius of 3 cm undergoes a dilation with a scale factor 'k'. What is the new radius of the circle?

Accepted Answer

3k cm

Answer

k cm

Answer

3 / k cm

Answer

k^2 cm

Question 19

When a figure undergoes dilation with a scale factor less than one, what happens to its perimeter?

Accepted Answer

Decreases

Answer

Increases

Answer

Stays the same

Answer

Increases by the scale factor

Question 20

What is a glide reflection? Provide an example of a transformation that can be described as a glide reflection.

Accepted Answer

Sliding a figure along a line and then reflecting it across a perpendicular line.

Answer

Rotating a figure around a fixed point.

Answer

Enlarging or reducing a figure.

Answer

Flipping a figure over a line.

Question 21

Beyond mathematical applications, how are transformations used in the real world?

Accepted Answer

Mapping and navigation systems

Accepted Answer

Designing and engineering structures

Accepted Answer

Creating special effects in movies and animations

Answer

Solving complex mathematical equations

Question 22

Identify the transformation represented by this matrix:

[cos(θ) -sin(θ)]
[sin(θ)  cos(θ)]

Accepted Answer

Rotation

Answer

Translation

Answer

Reflection

Answer

Shear

Question 23

How do translations impact the area and perimeter of a figure?

Accepted Answer

Both the area and perimeter remain the same.

Answer

The area remains the same, but the perimeter may change.

Answer

Both the area and perimeter increase.

Question 24

A figure undergoes reflection across the y-axis, followed by a translation of 5 units to the right. Describe its final position and orientation.

Accepted Answer

Reflected across the y-axis and shifted 5 units to the right

Answer

Reflected across the y-axis and shifted 5 units to the left

Answer

Shifted 5 units to the right and then reflected across the y-axis

Answer

Remains in its original position and orientation

Question 25

A square with a side length of 6 cm undergoes dilation by a scale factor of 3. What is the area of the dilated square?

Accepted Answer

108 cm²

Answer

6 cm²

Answer

36 cm²

Answer

324 cm²

Question 26

Which transformation preserves the shape and size of a figure?

Accepted Answer

Translation

Answer

Rotation

Answer

Reflection across a line

Answer

Dilatation

Question 27

A triangle is translated 5 units to the right. What are the coordinates of the new vertex if the original vertex was at (2, 4)?

Accepted Answer

(7, 4)

Answer

(5, 4)

Answer

(7, 1)

Answer

(5, 1)

Question 28

A triangle is reflected across the y-axis. Which of the following changes after the reflection?

Accepted Answer

Orientation

Answer

Length

Answer

Width

Answer

Area

Question 29

A square is dilated by a scale factor of 0.5. What is the area of the dilated square?

Accepted Answer

Half the area of the original square

Answer

Same as the area of the original square

Answer

Double the area of the original square

Answer

Quadruple the area of the original square

Question 30

How do transformations contribute to the structural symmetry of buildings and objects? Provide specific examples to support your answer.

Accepted Answer

Transformations can be used to create structural symmetry in buildings, enhancing both their visual appeal and structural stability.

Answer

Transformations are not used in architecture and design.

Answer

Transformations are only used to enhance the visual appeal of buildings, not their structural integrity.

Answer

Transformations can create structural symmetry in buildings, but this does not impact their visual aesthetics.

Question 31

Which option correctly explains the difference between a dilation and a similarity transformation?

Accepted Answer

A dilation changes the size of a figure, while a similarity transformation keeps the shape but not the size.

Answer

A dilation keeps the shape of a figure, while a similarity transformation changes both the shape and size.

Answer

Both dilations and similarity transformations keep the size and shape of a figure.

Answer

Both dilations and similarity transformations change the size and shape of a figure.

Question 32

A translation is represented by the vector (a, b). After applying this translation, what is the new location of point (x, y)?

Accepted Answer

(x + a, y + b)

Answer

(x - a, y - b)

Answer

(x, y + b)

Answer

(x + a, y)

Question 33

What happens to the area of a rectangle after it is reflected across a line?

Accepted Answer

Remains the same

Answer

Doubles

Answer

Halves

Answer

Cannot be determined

Question 34

Point (x, y) is reflected across the line y = x. What are the new coordinates of the point?

Accepted Answer

(y, x)

Answer

(x, -y)

Answer

(-x, y)

Answer

(-y, x)

Question 35

Which transformation is NOT considered rigid?

Accepted Answer

Dilation

Answer

Translation

Answer

Rotation

Answer

Reflection

Question 36

A triangle undergoes a dilation by a factor of 2. What happens to its perimeter?

Accepted Answer

Doubles

Answer

Remains the same

Answer

Halves

Answer

Cannot be determined

Question 37

Which transformation preserves both the distance and orientation of a figure?

Accepted Answer

Translation

Answer

Reflection

Answer

Rotation

Answer

Dilation

Question 38

How does the area of a figure change after a translation?

Accepted Answer

It remains unchanged.

Answer

It is doubled.

Answer

It is halved.

Answer

It is tripled.

Question 39

Which sequence of transformations will NOT result in a figure that is identical to the original figure?

Accepted Answer

Rotation, dilation, rotation

Answer

Translation, rotation, translation

Answer

Rotation, reflection, rotation

Answer

Translation, reflection, translation

Question 40

Which of the following is NOT a rigid transformation in geometry?

Accepted Answer

Enlargement

Answer

Translation

Answer

Rotation

Answer

Reflection

Question 41

How do transformations contribute to the symmetry found in buildings and objects?

Accepted Answer

Rotations and reflections create balanced and visually appealing designs.

Answer

Translations ensure structural stability and resistance to forces.

Answer

Transformations have no practical applications in architecture or design.

Answer

Only rotations can create symmetrical buildings and objects.

Question 42

Which transformation undoes a translation?

Accepted Answer

Translation

Answer

Rotation

Answer

Reflection

Answer

Dilation

Question 43

When a figure is moved 5 units to the right and 3 units up, what are the coordinates of its image if the original coordinates were (2, 4)?

Accepted Answer

(7, 7)

Answer

(2, 7)

Answer

(7, 4)

Answer

(0, 1)

Question 44

Which transformation creates a mirror image of a figure across a line?

Accepted Answer

Reflection

Answer

Translation

Answer

Rotation

Answer

Dilation

Question 45

If a figure is rotated 180 degrees around any point, what is the resulting image like?

Accepted Answer

Identical to the original figure

Answer

Similar but not identical to the original figure

Answer

Opposite to the original figure

Answer

Larger than the original figure

Question 46

Which of the following is NOT a rigid transformation?

Accepted Answer

Dilation

Answer

Translation

Answer

Rotation

Answer

Reflection

Question 47

If a triangle has vertices (2, 3), (4, 5), and (6, 3), and is reflected over the y-axis, what are the coordinates of its image?

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 48

A circle with center at the origin and radius 5 units is rotated 360 degrees about its center. What is the total angle of rotation?

Accepted Answer

360°

Answer

180°

Answer

270°

Answer

450°

Question 49

A quadrilateral is rotated 90 degrees counterclockwise around the origin. If the original coordinates of one of its vertices were (-2, 3), what would be the coordinates of its image?

Accepted Answer

(3, -2)

Answer

(-3, 2)

Answer

(3, 2)

Answer

(-3, -2)

Question 50

Which transformation results in a figure that is identical to the original but in a different location?

Accepted Answer

Translation

Answer

Reflection

Answer

Rotation

Answer

Dilation

Question 51

A rectangle is rotated 90 degrees counterclockwise around a fixed point. What is the resulting transformation?

Accepted Answer

Rotation

Answer

Reflection

Answer

Translation

Answer

Enlargement

Question 52

Which transformation creates a mirror image of a figure across a line?

Accepted Answer

Reflection

Answer

Rotation

Answer

Shear

Answer

Translation

Question 53

A triangle is reflected over the x-axis. What change occurs to the y-coordinates of its vertices?

Accepted Answer

They are negated (multiplied by -1).

Answer

They are halved.

Answer

They remain the same.

Answer

They are doubled.

Question 54

Which of the following transformations does NOT preserve the size and shape of a figure?

Accepted Answer

Dilation

Answer

Translation

Answer

Reflection

Answer

Rotation

Question 55

Which transformation maintains the handedness (left or right-facing) of a figure?

Accepted Answer

Rotation

Answer

Shear

Answer

Translation

Answer

Reflection

Question 56

A triangle is translated 4 units up. What are the coordinates of its new vertices if the original coordinates were (2, 3), (4, 6), and (6, 3)?

Accepted Answer

(2, 7), (4, 10), (6, 7)

Answer

(6, 3), (8, 6), (10, 3)

Answer

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

Answer

(2, -1), (4, 2), (6, -1)

Question 57

Which of the following is formed by applying one transformation after another?

Accepted Answer

Composite transformation

Answer

Rigid transformation

Answer

Inverse transformation

Answer

Single transformation

Question 58

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

Accepted Answer

(-1, 1), (-4, 1), (-4, 3), (-1, 3)

Answer

(1, 1), (4, 1), (4, 3), (1, 3)

Answer

(3, 1), (0, 1), (0, 3), (3, 3)

Answer

(1, -1), (4, -1), (4, -3), (1, -3)

Question 59

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

Accepted Answer

12 units

Answer

6 units

Answer

24 units

Answer

18 units

Question 60

Which transformation preserves both the size and shape of a figure?

Accepted Answer

Translation

Answer

Reflection

Answer

Rotation

Answer

Dilation

Question 61

A square with side length 6 units is dilated by a scale factor of 1/2. What is the perimeter of the image of the square?

Accepted Answer

12 units

Answer

36 units

Answer

24 units

Answer

6 units

Question 62

A circle with a radius of 4 units is dilated by a scale factor of 3. What is the area of the image of the circle?

Accepted Answer

144π square units

Answer

36π square units

Answer

48π square units

Answer

16π square units

Question 63

A rigid motion that moves every point of a figure the same distance in the same direction is called a:

Accepted Answer

Translation

Answer

Rotation

Answer

Dilation

Answer

Reflection

Question 64

Which transformation creates a mirror image of a figure?

Accepted Answer

Reflection

Answer

Translation

Answer

Rotation

Answer

Dilation