Master Geometric Transformations: Translation, Reflection, Rotation, and Dilation

Question 1

After a dilation with a scale factor of 2, the point (2, 3) is translated 3 units to the right. What are the coordinates of the final image?

Accepted Answer

(7, 6)

Answer

(4, 6)

Answer

(7, 3)

Answer

(4, 3)

Question 2

Which of the following changes when a figure is reflected over a line of reflection?

Accepted Answer

Orientation

Answer

Size

Answer

Shape

Answer

Distance from the line of reflection

Question 3

If the coordinates of a point are (3, 4) and it is translated 2 units to the right and 1 unit down, what are its new coordinates?

Accepted Answer

(5, 3)

Answer

(1, 3)

Answer

(5, 5)

Answer

(1, 5)

Question 4

A figure is reflected over the y-axis. Which of the following points will NOT change as a result of this transformation?

Accepted Answer

(0, 5)

Answer

(2, 3)

Answer

(-2, 3)

Answer

(4, -1)

Question 5

When performing a translation, the figure is moved from its original position:

Accepted Answer

Along a line

Answer

Perpendicular to a line

Answer

Around a point

Answer

By a certain scalar factor

Question 6

A reflection over the y-axis will result in:

Accepted Answer

Flipping the figure across a vertical line

Answer

Flipping the figure across a horizontal line

Answer

Enlarging the figure

Answer

Reducing the figure

Question 7

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

Accepted Answer

9 : 1

Answer

1 : 3

Answer

3 : 1

Answer

1 : 9

Question 8

Which of the following transformations changes the size of a figure?

Accepted Answer

Dilation

Answer

Translation

Answer

Reflection

Answer

Rotation

Question 9

Which transformation creates a mirror image of a figure with respect to a line?

Accepted Answer

Reflection

Answer

Translation

Answer

Rotation

Answer

Dilation

Question 10

If a figure is rotated 180 degrees counterclockwise around the origin, what is the angle of rotation?

Accepted Answer

180 degrees

Answer

-180 degrees

Answer

90 degrees

Answer

270 degrees

Question 11

Which of the following is a composite transformation that is equivalent to a rotation?

Accepted Answer

Reflection followed by a reflection

Answer

Rotation followed by a dilation

Answer

Translation followed by a rotation

Answer

Dilation followed by a reflection

Question 12

To translate a point (x, y) by (a, b), which rule should you apply?

Accepted Answer

(x + a, y + b)

Answer

(x - a, y - b)

Answer

(x, y + a)

Answer

(x, y - b)

Question 13

To find the reflection of the line y = 2x over the x-axis, which equation should you use?

Accepted Answer

y = -2x

Answer

y = 2x

Answer

x = -2y

Answer

x = 2y

Question 14

To double the length of each side of a figure using dilation, what scale factor should be used?

Accepted Answer

2

Answer

0.5

Answer

1

Answer

4

Question 15

What is the name of the line used as a reference for reflection?

Accepted Answer

Axis of reflection

Answer

Axis of rotation

Answer

Translation vector

Answer

Dilation center

Question 16

Which type of transformation is not considered rigid?

Accepted Answer

Dilation

Answer

Translation

Answer

Reflection

Answer

Rotation

Question 17

Which point will remain unchanged after translation?

Accepted Answer

(0, 0)

Answer

(2, 3)

Answer

(5, -1)

Answer

(-4, 6)

Question 18

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

Rotate the figure by 180 degrees

Answer

Reflect the figure over a line

Question 19

What is the center of rotation for a rotation of 90 degrees counterclockwise around the point (3, 4)?

Accepted Answer

(3, 4)

Answer

(4, 3)

Answer

(6, 7)

Answer

(7, 6)

Question 20

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

Accepted Answer

Dilation with scale factor less than 1

Answer

Reflection

Answer

Rotation

Answer

Translation

Question 21

Which of the following correctly represents a rotation transformation of 90° counterclockwise around the origin?

Accepted Answer

R(90°)

Answer

R(-90°)

Answer

R(270°)

Answer

R(180°)

Question 22

A figure is reflected over the y-axis. What is the sign of the x-coordinate of its image?

Accepted Answer

Negative

Answer

Positive

Answer

Zero

Answer

Depends on the original point

Question 23

Which transformation reverses the orientation of a figure?

Accepted Answer

Reflection

Answer

Translation

Answer

Rotation

Answer

Dilation

Question 24

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

Accepted Answer

12 units

Answer

4 units

Answer

6 units

Answer

8 units

Question 25

A triangle with vertices at (1, 2), (3, 4), and (5, 2) is translated 3 units to the left and 2 units down. What are the coordinates of the image of the triangle?

Accepted Answer

(-2, 0), (0, 2), (2, 0)

Answer

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

Answer

(2, 0), (4, 2), (6, 0)

Answer

(-2, 4), (0, 6), (2, 4)

Question 26

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

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 27

A square with vertices at (0, 0), (2, 0), (2, 2), and (0, 2) is rotated 90 degrees counterclockwise about the origin. What are the coordinates of the image of the square?

Accepted Answer

(0, 0), (0, 2), (-2, 2), (-2, 0)

Answer

(0, 0), (-2, 0), (-2, -2), (0, -2)

Answer

(-2, 2), (-2, 0), (0, 0), (0, 2)

Answer

(0, 0), (0, -2), (2, -2), (2, 0)

Question 28

A rectangle with vertices at (1, 1), (3, 1), (3, 2), and (1, 2) is dilated by a scale factor of 2 with the origin as the center of dilation. What are the coordinates of the image of the rectangle?

Accepted Answer

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

Answer

(0.5, 0.5), (1.5, 0.5), (1.5, 1), (0.5, 1)

Answer

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

Answer

(4, 4), (6, 4), (6, 6), (4, 6)

Question 29

Which transformation preserves both shape and size of a figure?

Accepted Answer

Translation

Answer

Dilation

Answer

Rotation

Answer

Reflection

Question 30

A triangle is reflected across the line y = x. Which of the following statements 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 similar but not congruent to the original triangle.

Answer

The image is smaller than the original triangle.

Question 31

A figure is rotated 180 degrees about the origin. What is the relationship between the original figure and its image?

Accepted Answer

The image is a reflection of the original figure across the origin.

Answer

The image is a translation of the original figure.

Answer

The image is a dilation of the original figure.

Question 32

A circle is dilated by a scale factor of 1/2. How does the radius of the image compare to the radius of the original circle?

Accepted Answer

The radius of the image is half the radius of the original circle.

Answer

The radius of the image is twice the radius of the original circle.

Answer

The radius of the image is the same as the radius of the original circle.

Question 33

A square with side length 4 is translated 3 units to the right and 2 units down. What is the area of the image of the square?

Accepted Answer

16 square units

Answer

12 square units

Answer

20 square units

Answer

24 square units

Question 34

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

Accepted Answer

The same as the perimeter of the original triangle.

Answer

Twice the perimeter of the original triangle.

Answer

Half the perimeter of the original triangle.

Question 35

Which of the following transformations will NOT change the size or shape of a figure?

Accepted Answer

Translation

Answer

Rotation

Answer

Dilation

Answer

Reflection

Question 36

A figure is reflected across the y-axis. Which of the following coordinates would remain the same?

Accepted Answer

(0, 5)

Answer

(5, -2)

Answer

(2, 3)

Answer

(-4, 1)

Question 37

A square is rotated 90 degrees counterclockwise around the origin. What is the new orientation of the square?

Accepted Answer

Rotated 90 degrees clockwise

Answer

Rotated 90 degrees counterclockwise

Answer

Rotated 180 degrees

Question 38

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

Accepted Answer

1:4

Answer

2:1

Answer

1:2

Answer

4:1

Question 39

Which transformation does NOT preserve distance?

Accepted Answer

Dilation

Answer

Translation

Answer

Rotation

Answer

Reflection

Question 40

A figure is translated 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

(5, 7)

Question 41

A triangle is reflected across the line y = 3. What is the equation of the line of reflection for its image?

Accepted Answer

y = -3

Answer

y = 0

Answer

x = -3

Answer

x = 3

Question 42

A circle is rotated 120 degrees clockwise around the point (-2, 5). What are the coordinates of the center of the circle's image?

Accepted Answer

(-4, 5)

Answer

(0, 5)

Answer

(-2, 7)

Answer

(-2, 3)

Question 43

A rectangle is dilated by a scale factor of 0.5. What is the ratio of the perimeter of the original rectangle to the perimeter of the dilated rectangle?

Accepted Answer

2:1

Answer

1:2

Answer

4:1

Question 44

A figure is transformed by a combination of a translation and a reflection. Which of the following sequences of transformations would NOT produce the same result?

Accepted Answer

Reflection followed by translation

Answer

Translation followed by reflection

Answer

Translation followed by translation

Answer

Reflection followed by reflection

Question 45

A quadrilateral is reflected across the y-axis. Which of the following statements is true about the image?

Accepted Answer

The image is congruent to the original quadrilateral.

Answer

The image is smaller than the original quadrilateral.

Answer

The image is larger than the original quadrilateral.

Question 46

A square with side length 4 is rotated 90 degrees clockwise about its center. What is the length of the diagonal of the image?

Accepted Answer

4√2

Answer

2√2

Answer

4

Answer

8

Question 47

A triangle is dilated with a scale factor of 2. Which of the following statements is NOT true about the image?

Accepted Answer

The perimeter of the image is twice the perimeter of the original triangle.

Answer

The image is similar to the original triangle.

Answer

The angles of the image are congruent to the angles of the original triangle.

Question 48

A rectangle with vertices A(1, 2), B(4, 2), C(4, 1), and D(1, 1) is reflected across the line y = x. What are the coordinates of the image of point A?

Accepted Answer

(2, 1)

Answer

(-1, 2)

Answer

(2, -1)

Answer

(1, -2)

Question 49

A circle with center (2, 3) and radius 5 is translated 4 units to the left and 2 units up. What are the coordinates of the center of the image?

Accepted Answer

(-2, 5)

Answer

(-2, 1)

Answer

(6, 1)

Answer

(6, 5)

Question 50

A triangle is rotated 180 degrees about the origin. Which of the following statements is true about the image?

Accepted Answer

The image is congruent to the original triangle.

Answer

The image is a dilation of the original triangle.

Answer

The image is a reflection of the original triangle.

Answer

The image is a translation of the original triangle.

Question 51

A square with side length 6 is dilated with a scale factor of 1/3. What is the area of the image?

Accepted Answer

4

Answer

12

Answer

36

Question 52

A pentagon is reflected across the x-axis. What is the effect of this transformation on the coordinates of the vertices?

Accepted Answer

The x-coordinates remain the same, and the y-coordinates are negated.

Answer

Both the x-coordinates and y-coordinates are negated.

Answer

The y-coordinates remain the same, and the x-coordinates are negated.

Question 53

A triangle is rotated 90 degrees counterclockwise about the origin. If the original triangle has vertices at (1, 2), (3, 1), and (2, 4), what are the coordinates of the image of the vertex at (3, 1)?

Accepted Answer

(-1, 3)

Answer

(3, -1)

Answer

(-3, 1)

Answer

(1, -3)