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

Question 1

Which transformation moves a figure without changing its size, shape, or orientation?

Accepted Answer

Translation

Answer

Rotation

Answer

Reflection

Answer

Dilation

Question 2

What is the center of rotation when a figure is rotated 180 degrees?

Accepted Answer

The center of the figure

Answer

The midpoint of the figure

Answer

The point furthest from the axis of rotation

Answer

The point closest to the axis of rotation

Question 3

Which transformation flips a figure over a line?

Accepted Answer

Reflection

Answer

Translation

Answer

Rotation

Answer

Dilation

Question 4

What is the scale factor when a figure is dilated by a factor of 2?

Accepted Answer

2

Answer

0.5

Answer

1

Answer

4

Question 5

Which transformation is a combination of a translation and a rotation?

Accepted Answer

Glide reflection

Answer

Dilation

Answer

Rotation

Answer

Reflection

Question 6

What is the image of the point (2, 3) after a translation of 5 units to the right and 2 units down?

Accepted Answer

(7, 1)

Answer

(7, 5)

Answer

(2, 1)

Answer

(2, 5)

Question 7

What is the angle of rotation when a figure is rotated 90 degrees clockwise about the origin?

Accepted Answer

90

Answer

180

Answer

270

Answer

360

Question 8

Which transformation is the inverse of a reflection?

Accepted Answer

Reflection

Answer

Translation

Answer

Rotation

Answer

Dilation

Question 9

Which of the following is NOT a rigid transformation?

Accepted Answer

Dilation

Answer

Translation

Answer

Rotation

Answer

Reflection

Question 10

Which type of transformation involves a flip across a line?

Accepted Answer

Reflection

Answer

Translation

Answer

Rotation

Answer

Dilation

Question 11

How is the area of a figure affected by a dilation?

Accepted Answer

It is increased by a factor equal to the scale factor squared.

Answer

It is decreased by a factor equal to the scale factor squared.

Answer

It remains the same.

Answer

It is increased by a factor equal to the scale factor.

Question 12

What is the possible range of angles for a rotation transformation?

Accepted Answer

0 to 360 degrees

Answer

0 to 90 degrees

Answer

0 to 180 degrees

Answer

-180 to 180 degrees

Question 13

What is the point of rotation for a 90-degree rotation around the origin?

Accepted Answer

The origin

Answer

The point being rotated

Answer

The midpoint of the line segment connecting the initial and final positions of the point

Answer

The centroid of the figure

Question 14

Which of the following is NOT a characteristic of a reflection transformation?

Accepted Answer

Involves a rotation of 180 degrees

Answer

Flips a figure across a line

Answer

Preserves distance and angle measure

Answer

Produces a congruent image

Question 15

What is the scale factor of a dilation that triples the length of a side?

Accepted Answer

3

Answer

1

Answer

2

Answer

4

Question 16

Which transformation alters the dimensions of a geometric shape?

Accepted Answer

Dilation

Answer

Translation

Answer

Rotation

Answer

Reflection

Question 17

A rotation of 90° clockwise around the origin maps point (2, 3) to which new point?

Accepted Answer

(3, -2)

Answer

(-2, 3)

Answer

(-3, -2)

Answer

(2, -3)

Question 18

Which characteristic is unique to a dilation?

Accepted Answer

Changes size

Answer

Preserves shape

Answer

Changes orientation

Answer

Maps points to corresponding points

Question 19

Which of the following transformations is NOT a similarity transformation?

Accepted Answer

Translation

Answer

Rotation

Answer

Dilation

Answer

Reflection

Question 20

Which transformation does NOT preserve the distance between points?

Accepted Answer

Dilation

Answer

Translation

Answer

Rotation

Answer

Reflection

Question 21

What transformation describes moving a shape 5 units upward?

Accepted Answer

Translation

Answer

Rotation

Answer

Reflection

Answer

Dilation

Question 22

Which transformation can alter the size of a shape?

Accepted Answer

Dilation

Answer

Translation

Answer

Rotation

Answer

Reflection

Question 23

What is the equation of the line of reflection for the transformation that maps (2, 5) to (2, -5)?

Accepted Answer

y = -2

Answer

y = 2

Answer

x = 2

Answer

x = -2

Question 24

A rectangle with vertices A(2, 3), B(5, 3), C(5, 6), and D(2, 6) undergoes dilation by a factor of 2 with the origin as the center. What are the coordinates of the dilated rectangle?

Accepted Answer

A'(4, 6), B'(10, 6), C'(10, 12), D'(4, 12)

Answer

A'(1, 1.5), B'(2.5, 1.5), C'(2.5, 3), D'(1, 3)

Answer

A'(0, 3), B'(2, 3), C'(2, 6), D'(0, 6)

Answer

A'(2, 0), B'(5, 0), C'(5, 2), D'(2, 2)

Question 25

Which type of transformation can flip a shape across a line?

Accepted Answer

Reflection

Answer

Translation

Answer

Rotation

Answer

Dilation

Question 26

What is the center of rotation for a transformation that rotates a square 180 degrees?

Accepted Answer

The intersection of the diagonals of the square

Answer

Any vertex of the square

Answer

The midpoint of a side of the square

Answer

A point outside the square

Question 27

Which of the following transformations is NOT a rigid transformation?

Accepted Answer

Dilation

Answer

Translation

Answer

Rotation

Answer

Reflection

Question 28

Which transformation preserves the distance between points?

Accepted Answer

Translation

Answer

Rotation

Answer

Reflection

Answer

Dilation

Question 29

What is the equation of the line that results when the line $y = x$ is reflected over the x-axis?

Accepted Answer

$y = -x$

Answer

$y = x$

Answer

$x = y$

Answer

$x = -y$

Question 30

The perimeter of a square with a side length of 5 units is dilated by a scale factor of 2. What is the perimeter of the resulting square?

Accepted Answer

40 units

Answer

10 units

Answer

20 units

Answer

80 units

Question 31

Which transformation is NOT considered rigid?

Accepted Answer

Dilation

Answer

Translation

Answer

Rotation

Answer

Reflection

Question 32

Which of the following is NOT a type of geometric transformation?

Accepted Answer

Stretching

Answer

Translation

Answer

Rotation

Answer

Reflection

Question 33

When a shape is translated 5 units to the right, its x-coordinates will change by:

Accepted Answer

5 units to the right

Answer

5 units to the left

Answer

10 units to the right

Answer

10 units to the left

Question 34

Which transformation can flip a shape over a line?

Accepted Answer

Reflection

Answer

Translation

Answer

Rotation

Answer

Dilation

Question 35

A dilation with a scale factor less than 1 will produce a shape that is:

Accepted Answer

Smaller than the original

Answer

Larger than the original

Answer

Congruent to the original

Answer

Rotated from the original

Question 36

A sequence of transformations is applied to a shape, starting with a translation and followed by a rotation. Which transformation should be performed first to maintain the original shape?

Accepted Answer

Translation

Answer

Rotation

Answer

Both transformations can be performed first

Answer

The order does not matter

Question 37

In a translation, which component specifies the starting point of the movement?

Accepted Answer

Coordinate pair

Answer

Magnitude

Answer

Direction

Answer

Line of reflection

Question 38

What is the angle of rotation for a full turn?

Accepted Answer

360 degrees

Answer

90 degrees

Answer

180 degrees

Answer

270 degrees

Question 39

Which of the following is NOT a type of reflection?

Accepted Answer

Circle reflection

Answer

Line reflection

Answer

Point reflection

Answer

Plane reflection

Question 40

In a dilation, what factor determines how much the figure is enlarged or reduced?

Accepted Answer

Scale factor

Answer

Translation vector

Answer

Rotation angle

Answer

Reflection line

Question 41

Which type of transformation preserves the distance between any two points?

Accepted Answer

Translation

Answer

Rotation

Answer

Reflection

Answer

Dilation

Question 42

What is the slope of the image of a figure reflected over the x-axis?

Accepted Answer

Negative

Answer

Positive

Answer

0

Answer

Undefined

Question 43

If 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

Answer

1/2

Answer

1

Answer

2

Question 44

Identify the option that is NOT a type of geometric transformation?

Accepted Answer

Scaling

Answer

Translation

Answer

Rotation

Answer

Dilation

Question 45

Which option correctly describes a rotation of 90 degrees counterclockwise about the origin?

Accepted Answer

x' = -y and y' = x

Answer

x' = x and y' = -y

Answer

x' = y and y' = -x

Answer

x' = -x and y' = y

Question 46

A figure is reflected over the x-axis. Which point among the following will remain fixed after the reflection?

Accepted Answer

(3, 2)

Answer

(2, 3)

Answer

(2, -3)

Answer

(3, -2)

Question 47

A rectangle with vertices A(0, 2), B(2, 2), C(2, 0), and D(0, 0) undergoes a dilation with a scale factor of 3. Determine the coordinates of the dilated rectangle.

Accepted Answer

A'(0, 6), B'(6, 6), C'(6, 0), D'(0, 0)

Answer

A'(0, 3), B'(3, 3), C'(3, 0), D'(0, 0)

Answer

A'(0, 2), B'(2, 6), C'(6, 0), D'(0, 0)

Answer

A'(0, 2), B'(2, 2), C'(2, 0), D'(0, 6)

Question 48

What does a translation transformation involve?

Accepted Answer

Moving a figure along a straight line without changing its size or shape.

Answer

Rotating a figure around a fixed point.

Answer

Flipping a figure over a straight line.

Answer

Enlarging or shrinking a figure.

Question 49

Which equation represents a horizontal line of reflection?

Accepted Answer

y = 0

Answer

y = x

Answer

y = -x

Answer

x = 0

Question 50

If a figure is rotated 270 degrees counterclockwise around the point (1, 4), what are the coordinates of the image of the point (3, 2)?

Accepted Answer

(-2, 3)

Answer

(-2, -3)

Answer

(2, -3)

Answer

(2, 3)

Question 51

What is the effect of a dilation transformation with a scale factor of 3 on the area of a figure?

Accepted Answer

Area is tripled.

Answer

Area is halved.

Answer

Area is quadrupled.

Answer

Area is unchanged.

Question 52

Which of the following is NOT a characteristic of a dilation transformation?

Accepted Answer

Changes the shape of a figure.

Answer

Enlarges or reduces a figure.

Answer

Preserves angles.

Answer

Preserves distances.

Question 53

Which of the following is NOT a geometric transformation?

Accepted Answer

Scaling

Answer

Translation

Answer

Rotation

Answer

Reflection

Question 54

A translation moves a figure:

Accepted Answer

Along a line without changing its orientation

Answer

Around a point without changing its size or shape

Answer

Across a line without changing its size or shape

Answer

Along a curve without changing its orientation

Question 55

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

Increase the size of the figure by 4 times

Answer

Decrease the size of the figure by 4 times

Question 56

Which of the following is a composite transformation?

Accepted Answer

Combination of a translation and a rotation

Answer

Translation of 5 units to the right

Answer

Rotation of 90 degrees about the origin

Answer

Reflection across the y-axis

Question 57

What is the inverse of a dilation with a scale factor of 1/2?

Accepted Answer

Dilation with a scale factor of 2

Answer

Translation of 2 units to the right

Answer

Rotation of 180 degrees about the origin

Answer

Reflection across the y-axis

Question 58

What are the two components that determine a translation?

Accepted Answer

Magnitude and direction

Answer

Length and angle

Answer

Speed and time

Answer

Force and distance

Question 59

When rotating a figure, what is the fixed point about which the figure turns called?

Accepted Answer

Center of rotation

Answer

Radius of rotation

Answer

Angle of rotation

Answer

Axis of rotation

Question 60

What happens to a figure when it undergoes a dilation with a scale factor less than 1?

Accepted Answer

Reduces the figure

Answer

Enlarges the figure

Answer

Rotates the figure

Answer

Flips the figure

Question 61

Which transformation maps triangle ABC onto triangle A'B'C'?

Accepted Answer

Translation 5 units right and 3 units up

Answer

Rotation 90 degrees counterclockwise about the origin

Answer

Reflection over the x-axis

Answer

Dilation with a scale factor of 2

Question 62

When a figure undergoes a translation followed by a rotation, in which order do these transformations occur?

Accepted Answer

Translation, then rotation

Answer

Rotation, then translation

Answer

Both transformations occur simultaneously

Answer

The order does not matter

Question 63

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

Accepted Answer

9:1

Answer

1:3

Answer

3:1

Answer

1:9

Question 64

Which transformation does NOT preserve distance?

Accepted Answer

Dilation

Answer

Translation

Answer

Rotation

Answer

Reflection