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

Question 1

Which of these statements about geometric transformations is **FALSE**?

Accepted Answer

Transformations always preserve angles.

Answer

Transformations can change the size of a figure.

Answer

Transformations can change the orientation of a figure.

Answer

Transformations can preserve distances.

Question 2

A dilation with a scale factor of more than 1 will

Accepted Answer

Enlarge the figure

Answer

Reflect the figure

Answer

Reduce the figure

Answer

Rotate the figure

Question 3

The area of a square is tripled by a dilation.

Accepted Answer

The scale factor is √3

Answer

The scale factor is 6

Answer

The scale factor is 1 / √3

Answer

The scale factor is 3

Question 4

Which transformation changes the size of a figure?

Accepted Answer

Dilation

Answer

Rotation

Answer

Reflection

Answer

Translation

Question 5

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

Accepted Answer

(7, 5)

Answer

(7, 2)

Answer

(5, 2)

Answer

(2, 5)

Question 6

A rotation of 180 degrees around the origin is equivalent to:

Accepted Answer

Reflection over both the x-axis and y-axis

Answer

Reflection over the x-axis only

Answer

Reflection over the y-axis only

Answer

Translation by (0, 180)

Question 7

Which transformation does not preserve the size of a figure?

Accepted Answer

Dilation

Answer

Rotation

Answer

Translation

Answer

Reflection

Question 8

Given the line y = 2x + 1, what is the equation of its image after a reflection over the y-axis?

Accepted Answer

y = -2x + 1

Answer

y = x + 1

Answer

y = -2x - 1

Answer

y = 2x - 1

Question 9

Which of the following is true about a dilation with a scale factor less than 1?

Accepted Answer

The image will be smaller than the original figure.

Answer

The image will have the same size as the original figure.

Answer

The image will be larger than the original figure.

Question 10

Given the circle with center (0, 0) and radius 3, what is the equation of its image after a dilation with a scale factor of 2?

Accepted Answer

(x - 0)^2 + (y - 0)^2 = 12

Answer

(x - 0)^2 + (y - 0)^2 = 6

Answer

(x - 0)^2 + (y - 0)^2 = 3

Answer

(x - 0)^2 + (y - 0)^2 = 4

Question 11

What is the purpose of an inverse transformation?

Accepted Answer

To reverse the effect of an original transformation.

Answer

To preserve the size and shape of the original figure.

Answer

To create a larger version of the original figure.

Answer

To create a different type of transformation.

Question 12

A translation moves a figure from one point to another without altering its size or shape. Which of the following is the correct notation for a translation?

Accepted Answer

(x, y) -> (x + a, y + b)

Answer

(x, y) -> (ax, by)

Answer

(x, y) -> (x * a, y * b)

Question 13

A rotation transforms a figure around a fixed point. What is the angle of rotation required to map point (x, y) onto point (x, -y)?

Accepted Answer

180°

Answer

360°

Answer

270°

Answer

90°

Question 14

A reflection flips a figure across a line, creating a mirror image. If a line has an equation of y = x, what is the equation of the line of reflection for the transformation that maps (2, 3) to (3, 2)?

Accepted Answer

y = x

Answer

x = 2

Answer

y = -x

Answer

y = 3

Question 15

A dilation either increases or decreases the size of a figure without altering its shape. What is the scale factor for a dilation that transforms a figure with an area of 12 square units to a figure with an area of 48 square units?

Accepted Answer

4

Answer

2

Answer

8

Answer

6

Question 16

Which sequence of transformations maps point (2, 3) onto point (-3, -2)?

Accepted Answer

Translation: (x, y) -> (x - 5, y - 5); Reflection: y = x

Answer

Rotation: 90° clockwise; Dilation: scale factor = 2

Answer

Translation: (x, y) -> (x + 5, y + 5); Reflection: y = -x

Question 17

Which transformation is NOT an isometry?

Accepted Answer

Dilation

Answer

Translation

Answer

Rotation

Question 18

A figure is reflected across the x-axis and then translated 5 units to the right. What is the overall transformation?

Accepted Answer

A reflection followed by a translation

Answer

A single reflection

Answer

A dilation

Answer

A rotation

Question 19

A triangle has vertices at (1, 2), (3, 1), and (2, 4). If the triangle is rotated 180 degrees about the origin, what are the coordinates of the image of the vertex (3, 1)?

Accepted Answer

(-3, -1)

Answer

(3, -1)

Answer

(-3, 1)

Answer

(1, -3)

Question 20

A rectangle is reflected across the line y = x. What is true about the image?

Accepted Answer

The image is congruent to the original rectangle.

Answer

The image is a different shape than the original rectangle.

Answer

The image is smaller than the original rectangle.

Answer

The image is larger than the original rectangle.

Question 21

A square is dilated by a scale factor of 3. What is the ratio of the area of the dilated square to the area of the original square?

Accepted Answer

9:1

Answer

1:3

Answer

3:1

Question 22

Which transformation maps a figure onto itself?

Accepted Answer

Identity Transformation

Answer

Rotation

Answer

Dilation

Answer

Translation

Question 23

A translation moves a figure to the left by 3 units. What are the coordinates of the image of the point (2, 5)?

Accepted Answer

(-1, 5)

Answer

(-1, 8)

Answer

(0, 2)

Answer

(5, 2)

Question 24

A dilation with a scale factor of 2.5 maps the line segment AB onto A'B'. What is the ratio of A'B' to AB?

Accepted Answer

2.5

Answer

0.25

Answer

5

Answer

1.25

Question 25

A figure is first rotated 90 degrees counterclockwise about the origin and then translated 4 units to the right. Which transformation is equivalent to this composite transformation?

Accepted Answer

Rotation of 90 degrees counterclockwise about the point (4, 0)

Answer

Translation of 4 units to the left and then rotation of 90 degrees clockwise about the origin

Answer

Translation of 4 units to the right and then rotation of 90 degrees counterclockwise about the origin

Question 26

What is the inverse of a translation of 5 units to the left?

Accepted Answer

Translation of 5 units to the right

Answer

Translation of 5 units down

Answer

Reflection over the y-axis

Answer

Rotation of 90 degrees counterclockwise about the origin

Question 27

Given the points A(2, 3) and B(5, 7), what are the coordinates of the midpoint of the line segment AB?

Accepted Answer

(3.5, 5)

Answer

(5.5, 7)

Answer

(4, 6)

Answer

(2.5, 3)

Question 28

Which transformation will map the point (3, -2) to the point (3, 2)?

Accepted Answer

Translation

Answer

Rotation

Answer

Dilation

Answer

Reflection

Question 29

What is the image of the point (2, 3) after a rotation of 90 degrees counterclockwise around the origin?

Accepted Answer

(-3, 2)

Answer

(-2, 3)

Answer

(2, -3)

Answer

(3, -2)

Question 30

Given the line y = 2x + 1, what is the equation of the line that is the reflection of y = 2x + 1 over the x-axis?

Accepted Answer

y = -2x + 1

Answer

y = -2x - 1

Answer

y = 2x - 1

Question 31

Which transformation will produce a figure that is similar to the original figure but larger?

Accepted Answer

Dilation

Answer

Reflection

Answer

Translation

Answer

Rotation

Question 32

What is the scale factor of a dilation that transforms a circle with a radius of 3 units to a circle with a radius of 6 units?

Accepted Answer

2

Answer

5

Answer

3

Answer

4

Question 33

Which transformation will preserve the orientation of a figure?

Accepted Answer

Translation

Answer

Dilation

Answer

Reflection

Answer

Rotation

Question 34

What is the image of the triangle with vertices (1, 2), (3, 4), and (5, 2) after a translation of 3 units to the right?

Accepted Answer

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

Answer

(0, 2), (2, 4), (4, 2)

Answer

(1, 1), (3, 3), (5, 1)

Answer

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

Question 35

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

Accepted Answer

(-3, 2)

Answer

(-2, 3)

Answer

(2, 3)

Answer

(3, -2)

Question 36

Which transformation can be used to map a rectangle to a parallelogram?

Accepted Answer

Translation

Answer

Dilation

Answer

Reflection

Answer

Rotation