Transformations in Geometry: Master the Art of Geometric Transformations

Question 1

Find the transformation matrix for a dilation with a scale factor of 3 centered at the origin.

Accepted Answer

[3 0 0][0 3 0][0 0 1]

Answer

[1/3 0 0][0 1/3 0][0 0 1]

Answer

[3 0 0][0 1/3 0][0 0 1]

Answer

[1/3 0 0][0 3 0][0 0 1]

Question 2

Which of the following is not a recognized transformation in geometry?

Accepted Answer

Enlargement

Answer

Translation

Answer

Rotation

Answer

Reflection

Question 3

A translation moves a figure:

Accepted Answer

Along a straight line without changing its size or shape

Answer

Around a fixed point without changing its size or shape

Answer

Over a line of symmetry without changing its size or shape

Answer

By a factor, changing its size but not its shape

Question 4

A figure is translated 5 units to the right and 3 units down. What are the coordinates of the image of a point (2, 4)?

Accepted Answer

(7, 7)

Answer

(7, 1)

Answer

(-3, 1)

Answer

(-3, 7)

Question 5

A figure is rotated 180 degrees about the origin. What is the effect on the coordinates of a point?

Accepted Answer

The signs of both coordinates change

Answer

Only the x-coordinate changes sign

Answer

Only the y-coordinate changes sign

Answer

The coordinates remain unchanged

Question 6

Which of the following is a real-world example of a dilation?

Accepted Answer

Zooming in on a photograph

Answer

Flipping a figure over

Answer

Sliding a figure along a line

Answer

Rotating a figure around a point

Question 7

Which transformation does NOT maintain the size and shape of a figure?

Accepted Answer

Dilation

Answer

Translation

Answer

Rotation

Answer

Reflection

Question 8

In a translation, a figure is moved:

Accepted Answer

Along a straight line

Answer

Around a fixed point

Answer

Over a reflection line

Answer

To a different size

Question 9

A reflection about the y-axis:

Accepted Answer

Changes the y-coordinates of points

Answer

Changes the x-coordinates of points

Answer

Changes both coordinates of points

Answer

Does not change the coordinates of points

Question 10

A dilation with a scale factor of 2 will:

Accepted Answer

Double the size of a figure

Answer

Halve the size of a figure

Answer

Increase the size by 2 units

Answer

Decrease the size by 2 units

Question 11

Reflect the triangle with vertices ((2, 3), (4, 7), (6, 3)) over the y-axis. Draw the resulting figure.

Accepted Answer

[(2, -1), (4, 3), (6, -1)]

Answer

[(2, 1), (4, 5), (6, 1)]

Answer

[(2, -3), (4, -7), (6, -3)]

Question 12

What is the rule for translating a point (x, y) 3 units to the right and 2 units up?

Accepted Answer

(x + 3, y + 2)

Answer

(x - 3, y + 2)

Answer

(x + 3, y - 2)

Answer

(x - 3, y - 2)

Question 13

Which transformation maps a figure onto itself?

Accepted Answer

Identity

Answer

Translation

Answer

Rotation

Answer

Reflection

Question 14

In geometric transformations, which operation involves sliding a figure from one location to another without changing its size or orientation?

Accepted Answer

Translation

Answer

Rotation

Answer

Reflection

Answer

Dilation

Question 15

When a figure is turned around a fixed point by 90 degrees in a clockwise direction, the transformation is known as:

Accepted Answer

Clockwise rotation

Answer

Counterclockwise rotation

Answer

Reflection

Answer

Dilation

Question 16

Which transformation creates a mirror image of a figure by flipping it over a line?

Accepted Answer

Reflection

Answer

Translation

Answer

Rotation

Answer

Dilation

Question 17

What is the effect of a dilation transformation when the scale factor is greater than 1?

Accepted Answer

Enlarges the figure

Answer

Shrinks the figure

Answer

Rotates the figure

Answer

Reflects the figure

Question 18

When applying a translation to a point (x, y) using the vector (a, b), what are the resulting coordinates?

Accepted Answer

(x + a, y + b)

Answer

(x - a, y - b)

Answer

(a - x, b - y)

Answer

(b - x, a - y)

Question 19

Which transformation can be used to create a figure that is symmetrical with respect to a line?

Accepted Answer

Reflection

Answer

Translation

Answer

Rotation

Answer

Dilation

Question 20

For two similar figures, what is the relationship between their areas?

Accepted Answer

Equal to the square of the ratio of their corresponding side lengths

Answer

Equal to the ratio of their corresponding side lengths

Answer

Equal to the product of the ratio of their corresponding side lengths

Answer

Equal to the difference of the ratio of their corresponding side lengths

Question 21

How do rigid transformations differ from non-rigid transformations in terms of their effects on shapes and sizes? Provide examples for each type.

Accepted Answer

Rigid transformations (like translations and rotations) keep both shape and size the same, while non-rigid transformations (like dilation) change one or both.

Answer

Rigid transformations change size but keep shape the same, while non-rigid transformations change both.

Answer

Non-rigid transformations keep shape the same but change size, while rigid transformations change both.

Answer

Both rigid and non-rigid transformations keep both shape and size the same.

Question 22

Which of the following transformations is NOT considered a rigid transformation?

Accepted Answer

Dilation

Answer

Translation

Answer

Rotation

Answer

Reflection

Question 23

When a point is translated, how do its coordinates change?

Accepted Answer

A constant is added to both coordinates.

Answer

A constant is subtracted from both coordinates.

Answer

Both coordinates are multiplied by a constant.

Answer

Both coordinates are divided by a constant.

Question 24

What type of transformation creates a mirror image of a figure over a line?

Accepted Answer

Reflection

Answer

Translation

Answer

Rotation

Answer

Dilation

Question 25

How does the area of a figure change after a dilation with a scale factor of 2?

Accepted Answer

It doubles.

Answer

It triples.

Answer

It quadruples.

Answer

It halves.

Question 26

After a rectangle is rotated 180 degrees around its center, how many lines of symmetry does it have?

Accepted Answer

4

Answer

0

Answer

2

Answer

8

Question 27

Which figure is NOT similar to the original figure after a dilation?

Accepted Answer

Circle

Answer

Triangle

Answer

Square

Answer

Rectangle

Question 28

The transformation rule (x, y) -> (-y, x) represents which transformation?

Accepted Answer

Reflection over the y-axis

Answer

Reflection over the x-axis

Answer

Rotation of 90 degrees clockwise

Answer

Rotation of 90 degrees counterclockwise

Question 29

A translation of a figure 3 units to the right and 5 units down is represented by the vector:

Accepted Answer

(3, -5)

Answer

(3, 5)

Answer

(-3, -5)

Answer

(-3, 5)

Question 30

A figure is first reflected across the x-axis and then translated 2 units to the right. The combined effect of these transformations is:

Accepted Answer

Reflection across the y-axis

Answer

Translation 2 units to the left

Answer

Rotation 180 degrees

Answer

Dilation by a scale factor of 1

Question 31

Which transformation is NOT considered a rigid transformation?

Accepted Answer

Dilation

Answer

Translation

Answer

Rotation

Answer

Reflection

Question 32

What type of transformation produces a mirror image of a figure?

Accepted Answer

Reflection

Answer

Translation

Answer

Dilation

Answer

Rotation

Question 33

A figure is rotated 90 degrees clockwise about the origin. What are the coordinates of the image of a point (3, -4)?

Accepted Answer

(-4, 3)

Answer

(3, 4)

Answer

(4, -3)

Question 34

Which transformation changes the size of a figure without changing its shape?

Accepted Answer

Dilation

Answer

Rotation

Answer

Translation

Answer

Reflection

Question 35

A figure is dilated by a scale factor of 2. What is the ratio of the area of the image to the area of the original figure?

Accepted Answer

4:1

Answer

1:2

Answer

2:1

Answer

1:4

Question 36

A translation is represented by the vector (a, b). What are the coordinates of the image of the point (x, y) after applying this transformation?

Accepted Answer

(x + a, y + b)

Answer

(x - a, y - b)

Answer

(a - x, b - y)

Answer

(y - a, x - b)

Question 37

Which of the following is a rotational symmetry of an equilateral triangle?

Accepted Answer

120 degrees

Answer

30 degrees

Answer

90 degrees

Answer

60 degrees

Question 38

Which of the following transformations can produce a figure that is larger than the original figure?

Accepted Answer

Dilation with a scale factor greater than 1

Answer

Reflection

Answer

Rotation

Answer

Translation

Question 39

Which of the following is NOT a rigid transformation?

Accepted Answer

Dilation

Answer

Reflection

Answer

Translation

Answer

Rotation

Question 40

Which of the following is an example of a composite transformation?

Accepted Answer

Rotation followed by a translation

Answer

Translation

Answer

Dilation

Answer

Reflection

Question 41

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

Accepted Answer

Translation

Answer

Reflection

Answer

Dilation

Answer

Rotation

Question 42

When a rectangle is reflected over the y-axis, which side remains unchanged?

Accepted Answer

Side parallel to the y-axis

Answer

All sides

Answer

Diagonal

Answer

Side parallel to the x-axis

Question 43

A dilation with a scale factor of 1/2 will:

Accepted Answer

Halve the perimeter and area

Answer

Double the perimeter only

Answer

Double the area only

Question 44

Which transformation maps a figure onto itself, resulting in no change?

Accepted Answer

Identity transformation

Answer

Translation

Answer

Reflection

Answer

Rotation

Question 45

If a triangle is translated 4 units to the left and 3 units up, what is the effect on the coordinates of its centroid?

Accepted Answer

It moves 4 units to the left and 3 units up

Answer

It moves 4 units to the right and 3 units down

Answer

It remains unchanged

Question 46

Which transformation can create an image that is congruent but not similar to the original figure?

Accepted Answer

Reflection

Answer

Translation

Answer

Rotation

Question 47

What is the inverse transformation of a dilation with a scale factor of 3?

Accepted Answer

Dilation with a scale factor of 1/3

Answer

Reflection over the x-axis

Answer

Rotation of 180 degrees

Answer

Translation with a negative vector

Question 48

Which of the following is a transformation that moves a figure from one point to another without changing its size or shape?

Accepted Answer

Translation

Answer

Rotation

Answer

Dilation

Answer

Reflection

Question 49

What is the effect of a 90-degree rotation about the origin on the point (3, 4)?

Accepted Answer

(-4, 3)

Answer

(-3, 4)

Answer

(3, -4)

Answer

(4, -3)

Question 50

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

Accepted Answer

The x-coordinate changes sign.

Answer

Both the x- and y-coordinates change sign.

Answer

The figure is enlarged or reduced.

Answer

The y-coordinate changes sign.

Question 51

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

Accepted Answer

√2

Answer

√3

Answer

3

Answer

2

Question 52

Which of the following sequences of transformations would result in a figure that is congruent to the original figure?

Accepted Answer

Translation followed by a rotation of 180 degrees

Answer

Reflection followed by a dilation

Answer

Dilation followed by a reflection

Answer

Rotation of 90 degrees followed by a reflection

Question 53

What is the image of the point (2, -3) after a reflection across the line y = x?

Accepted Answer

(-3, 2)

Answer

(-2, 3)

Answer

(3, 2)

Answer

(2, 3)

Question 54

Which of the following is not a rigid transformation?

Accepted Answer

Dilation

Answer

Rotation

Answer

Reflection

Answer

Translation

Question 55

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

Accepted Answer

The point that is fixed under the dilation

Answer

The point that is reflected under the dilation

Answer

The point that moves the most under the dilation

Answer

The point that is rotated under the dilation

Question 56

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

Accepted Answer

Rigid transformation

Answer

Non-rigid transformation

Answer

Affine transformation

Answer

Linear transformation

Question 57

What is the image of the triangle with vertices (0, 0), (3, 0), and (0, 4) after a dilation with a scale factor of 2 and a center at the origin?

Accepted Answer

Triangle with vertices (0, 0), (6, 0), and (0, 8)

Answer

Triangle with vertices (2, 2), (6, 2), and (2, 8)

Answer

Triangle with vertices (0, 0), (3, 3), and (0, 4)

Answer

Triangle with vertices (2, 0), (6, 0), and (2, 4)