Transformations in Geometry: Master the Art of Geometric Transformations

Question 1

What is the scale factor of a dilation that increases the area of a figure by a factor of 9?

Accepted Answer

9

Answer

2

Answer

3

Answer

6

Question 2

Which transformation would map a circle centered at the origin onto a circle with half the radius?

Accepted Answer

Dilation

Answer

Translation

Answer

Reflection

Answer

Rotation

Question 3

When a triangle undergoes a transformation across the y-axis, which of the following occurs?

Accepted Answer

Reflection across the y-axis

Answer

Translation

Answer

Reflection across the x-axis

Answer

Rotation by 180 degrees

Question 4

When reflecting a figure over which type of line will the resulting image be congruent to the original?

Accepted Answer

Perpendicular bisector

Answer

Parallel line

Answer

Intersecting line

Answer

Neither of the above

Question 5

What is the angle of rotation if a figure is flipped directly upside down?

Accepted Answer

180 degrees

Answer

90 degrees

Answer

270 degrees

Answer

360 degrees

Question 6

If a figure is translated 5 units to the right and 3 units up, what are the coordinates of its translated image?

Accepted Answer

(x + 5, y + 3)

Answer

(x - 5, y + 3)

Answer

(x + 5, y - 3)

Answer

(x - 5, y - 3)

Question 7

A dilation transformation with a scale factor greater than 1 will create an image that is:

Accepted Answer

Larger than the original

Answer

Smaller than the original

Answer

Identical to the original

Answer

Cannot be determined

Question 8

If a figure is translated 5 units upwards and 2 units to the right, what will be the coordinates of its translated image?

Accepted Answer

(2, 5)

Answer

(5, -2)

Answer

(-5, -2)

Answer

(-2, 5)

Question 9

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

Accepted Answer

Dilation

Answer

Translation

Answer

Reflection

Answer

Rotation

Question 10

To produce an equivalent transformation, a parallelogram is first translated 3 units to the left and then reflected over the x-axis. In which order should these transformations be performed?

Accepted Answer

Translation, then reflection

Answer

Reflection, then translation

Answer

Reflection, then rotation

Answer

Rotation, then reflection

Question 11

Which transformation will move a figure away from the origin?

Accepted Answer

Translation to the right

Answer

Reflection over the x-axis

Answer

Rotation 90 degrees clockwise

Answer

Dilation with a scale factor of less than 1

Question 12

Which of the following transformations is NOT an isometry?

Accepted Answer

Dilation

Answer

Translation

Answer

Reflection

Answer

Rotation about 90 degrees

Question 13

A square with vertices at (0, 0), (1, 0), (1, 1), and (0, 1) is translated 5 units to the right and 3 units up. What are the coordinates of its new vertices?

Accepted Answer

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

Answer

(5, 1), (6, 1), (6, 4), (5, 4)

Answer

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

Question 14

Which of the following transformations is NOT a rigid transformation?

Accepted Answer

Dilation

Answer

Translation

Answer

Reflection

Answer

Rotation about 90 degrees

Question 15

What is the center of rotation for a figure that is rotated 90 degrees clockwise around a specific point?

Accepted Answer

The point around which the rotation occurs

Answer

The origin

Answer

The midpoint of the figure

Answer

The center of gravity of the figure

Question 16

What is the angle of rotation for a figure that is rotated 180 degrees counterclockwise around a specific point?

Accepted Answer

180 degrees

Answer

90 degrees

Answer

270 degrees

Answer

360 degrees

Question 17

A circle has a radius of 6 centimeters. If the circle is dilated by a scale factor of 1/2, what will be the radius of the resulting figure?

Accepted Answer

3 centimeters

Answer

6 centimeters

Answer

9 centimeters

Answer

12 centimeters

Question 18

After translating a point 3 units to the right and 2 units up, what are the coordinates of its image?

Accepted Answer

(x + 3, y + 2)

Answer

(x - 3, y + 2)

Answer

(x + 3, y - 2)

Answer

(x - 3, y - 2)

Question 19

Which type of reflection flips a figure over a vertical line?

Accepted Answer

Reflection over the y-axis

Answer

Horizontal reflection

Answer

Vertical reflection

Answer

Reflection over the x-axis

Question 20

What is the angle of rotation for a transformation that turns a figure 3/4 of a full rotation counterclockwise?

Accepted Answer

270 degrees

Answer

90 degrees

Answer

180 degrees

Answer

360 degrees

Question 21

Which transformation results in an image that is smaller than the original figure?

Accepted Answer

Dilation with a scale factor less than 1

Answer

Dilation with a scale factor greater than 1

Answer

Translation

Answer

Rotation

Question 22

What transformation is equivalent to the composition of two reflections over parallel lines?

Accepted Answer

Translation

Answer

Rotation

Answer

Dilation

Answer

No transformation

Question 23

Which transformation does NOT preserve the shape of a figure?

Accepted Answer

Dilation

Answer

Translation

Answer

Reflection

Answer

Rotation

Question 24

What are the coordinates of the image of the point (2, -3) after a dilation with a scale factor of 3 and center at the origin?

Accepted Answer

(6, -9)

Answer

(2, -9)

Answer

(3, -9)

Answer

(6, -3)

Question 25

What type of transformation is a 90-degree rotation about a specific point?

Accepted Answer

Rotation

Answer

Translation

Answer

Reflection

Answer

Dilation

Question 26

Determine the inverse transformation of a translation of 5 units to the right along the x-axis.

Accepted Answer

Translation of 5 units to the left along the x-axis

Answer

Reflection over the y-axis

Answer

Rotation of 180 degrees about the origin

Question 27

Given the point (2, 5), what are the coordinates of its image after a translation of 3 units right and 2 units up?

Accepted Answer

(7, 7)

Answer

(5, 7)

Answer

(7, 5)

Answer

(5, 9)

Question 28

Which of the following lines is perpendicular to the line y = 2x + 3?

Accepted Answer

y = -1/2x

Answer

y = 2x

Answer

y = -2x

Answer

y = 1/2x

Question 29

Which of the following transformations is a combination of a translation and a reflection? (also known as a glide reflection)

Accepted Answer

Glide reflection

Answer

Dilation

Answer

Reflection

Answer

Translation

Question 30

Which of the following transformations maps a circle to an ellipse?

Accepted Answer

Dilation

Answer

Translation

Answer

Reflection

Answer

Rotation

Question 31

Which geometric transformation involves moving a figure parallel to the x-axis or y-axis?

Accepted Answer

Translation

Answer

Reflection

Answer

Rotation

Answer

Dilation

Question 32

When rotating a figure 90 degrees clockwise around the origin, what is the center of rotation?

Accepted Answer

(0, 0)

Answer

(1, 0)

Answer

(0, 1)

Answer

(-1, 0)

Question 33

Which transformation maintains both distance and angle measures?

Accepted Answer

Translation

Answer

Reflection

Answer

Rotation

Answer

Dilation

Question 34

After a reflection over the x-axis and then a 180-degree rotation around the origin, what is the overall transformation?

Accepted Answer

A reflection

Answer

A translation

Answer

A rotation

Answer

A dilation

Question 35

What is the result of a reflection over the y-axis?

Accepted Answer

Flips the figure vertically

Answer

Flips the figure horizontally

Answer

Rotates the figure 90 degrees

Answer

Enlarges the figure

Question 36

Which transformation changes the size of a figure but not its shape?

Accepted Answer

Dilation

Answer

Translation

Answer

Rotation

Answer

Reflection

Question 37

What is the center of dilation for a figure that is dilated by a scale factor of 3?

Accepted Answer

Any point within the figure

Answer

The point that is closest to the original figure

Answer

The point that is farthest from the original figure

Answer

There is no center of dilation

Question 38

Which of the following is not a transformation?

Accepted Answer

Area

Answer

Translation

Answer

Rotation

Answer

Reflection

Question 39

Which of the following transformations is a composition of a reflection and a translation?

Accepted Answer

Glide reflection

Answer

Rotation

Answer

Dilation

Answer

Translation

Question 40

Which of the following transformations preserves the distance between any two points in a figure?

Accepted Answer

Translation

Answer

Reflection

Answer

Rotation

Answer

Dilation

Question 41

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

Accepted Answer

They are negated (multiplied by -1).

Answer

They are doubled.

Answer

They are halved.

Answer

They remain unchanged.

Question 42

A dilation with a scale factor of 2 results in a figure that is:

Accepted Answer

Twice the size of the original figure.

Answer

Half the size of the original figure.

Answer

The same size as the original figure.

Answer

Three times the size of the original figure.

Question 43

A figure is dilated by a factor of 1/2. What is the ratio of the area of the dilated figure to the area of the original figure?

Accepted Answer

1/4

Answer

1/2

Answer

2

Answer

4

Question 44

When applying a combination of translation, rotation, and dilation transformations to a figure, which transformation should be applied last to preserve the orientation of the figure?

Accepted Answer

Dilation

Answer

Translation

Answer

Rotation

Answer

Reflection

Question 45

What is the effect of a dilation on the perimeter of a figure?

Accepted Answer

Increases the perimeter

Answer

Decreases the perimeter

Answer

Changes the shape

Answer

Does not affect the perimeter

Question 46

Which of the following describes a translation of a figure 3 units to the left and 2 units down?

Accepted Answer

(x, y) -> (x - 3, y - 2)

Answer

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

Answer

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

Answer

(x, y) -> (x, y + 2)

Question 47

What is the distance between the image and the preimage of a figure after a dilation with a scale factor of 2?

Accepted Answer

Twice the original distance

Answer

Half the original distance

Answer

Unchanged

Answer

Depends on the specific dilation

Question 48

Which of the following represents a dilation with a scale factor of 0.5?

Accepted Answer

(x, y) -> (0.5x, 0.5y)

Answer

(x, y) -> (2x, 2y)

Answer

(x, y) -> (x, 0.5y)

Answer

(x, y) -> (0.5x, y)

Question 49

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

Accepted Answer

Dilation

Answer

Translation

Answer

Reflection

Answer

Rotation

Question 50

A figure is translated 5 units to the right and 3 units up. What is the translation vector?

Accepted Answer

(5, 3)

Answer

(3, 5)

Answer

(-5, -3)

Answer

(-3, -5)

Question 51

Which of the following transformations would result in a figure that is three times as large as the original?

Accepted Answer

Dilation with a scale factor of 3

Answer

Translation

Answer

Reflection

Answer

Rotation

Question 52

What is the equation for the transformation that dilates a figure by a scale factor of 2?

Accepted Answer

(x, y) -> (2x, 2y)

Answer

(x, y) -> (1/2x, 1/2y)

Answer

(x, y) -> (x/2, y/2)

Answer

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

Question 53

What is the composite transformation that is equivalent to a translation of 4 units to the left followed by a reflection over the x-axis?

Accepted Answer

Reflection over the x-axis followed by a translation of 4 units to the right

Answer

Translation of 4 units to the right

Answer

Reflection over the y-axis

Answer

Translation of 4 units to the left followed by a reflection over the y-axis