Transformations in Geometry: Translations, Rotations, and Reflections

Question 1

Which transformation results in a new shape identical in size and shape to the original, but in a different position?

Accepted Answer

Translation

Answer

Rotation

Answer

Reflection

Question 2

If a shape is moved 5 units to the right and 3 units up, which rule describes this movement?

Accepted Answer

(x + 5, y + 3)

Answer

(x - 5, y - 3)

Answer

(x, y + 3)

Question 3

Which transformation produces a mirror image of the original shape?

Accepted Answer

Reflection

Answer

Translation

Answer

Rotation

Question 4

If a rectangle with vertices (2, 1), (4, 3), and (6, 1) is rotated 180 degrees around the origin, what are the new coordinates of its vertices?

Accepted Answer

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

Answer

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

Answer

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

Question 5

Which transformation changes the orientation of a shape without altering its size or shape?

Accepted Answer

Rotation

Answer

Translation

Answer

Reflection

Question 6

If a triangle with vertices (1, 1), (2, 2), and (3, 1) is reflected over the y-axis, what are the new coordinates of its vertices?

Accepted Answer

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

Answer

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

Answer

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

Question 7

What single transformation is equivalent to moving a shape 2 units to the right and then rotating it 90 degrees counterclockwise around the origin?

Accepted Answer

Translation 2 units to the right, then rotation 90 degrees counterclockwise around the origin

Answer

Translation 2 units to the right

Answer

Rotation 90 degrees counterclockwise around the origin

Answer

Rotation 90 degrees counterclockwise around the origin, then translation 2 units to the right

Question 8

What is meant by a transformation of a shape?

Accepted Answer

Moving, turning, or flipping the shape without changing its size or shape

Answer

Changing the shape's color or texture

Answer

Stretching or shrinking the shape to make it bigger or smaller

Answer

Cutting the shape into smaller pieces

Question 9

Which of the following is an example of a translation?

Accepted Answer

Sliding a shape to the left

Answer

Rotating a shape around a point

Answer

Flipping a shape over a line

Answer

Enlarging a shape

Question 10

What is the key difference between a rotation and a reflection?

Accepted Answer

A rotation turns a shape around a point, while a reflection flips a shape over a line.

Answer

A rotation flips a shape over a line, while a reflection turns a shape around a point.

Answer

A rotation moves a shape without changing its size or shape, while a reflection does.

Answer

There is no difference between a rotation and a reflection.

Question 11

Which of the following is NOT a property that is preserved under all transformations?

Accepted Answer

Volume

Answer

Length

Answer

Shape

Answer

Area

Question 12

True or False: A translation involves moving a shape along a straight line.

Accepted Answer

True

Answer

False

Question 13

What is the measure of the angle of rotation if a shape is turned a quarter turn clockwise?

Accepted Answer

90 degrees

Answer

45 degrees

Answer

180 degrees

Answer

270 degrees

Question 14

Which transformation does NOT alter the size or shape of a figure?

Accepted Answer

Translation

Answer

Rotation

Answer

Reflection

Answer

Dilation

Question 15

Which property remains unchanged under all transformations?

Accepted Answer

Congruence

Answer

Area

Answer

Perimeter

Answer

Parallelism

Question 16

A square is moved 3 units to the right. Which statement about the image is true?

Accepted Answer

It remains a square.

Answer

It is no longer a square.

Answer

Its perimeter has increased.

Answer

Its area has decreased.

Question 17

A rectangle is rotated 90 degrees clockwise. What is the relationship between the original and transformed rectangle?

Accepted Answer

They are similar but not congruent.

Answer

They are congruent.

Answer

They are neither congruent nor similar.

Answer

They overlap but are not congruent.

Question 18

Which transformation will produce an image that is larger than the original figure?

Accepted Answer

Dilation

Answer

Translation

Answer

Rotation

Answer

Reflection

Question 19

When a shape is translated, what happens to its shape?

Accepted Answer

It retains its original shape

Answer

Shape changes

Answer

Size changes

Answer

Both size and shape change

Question 20

In a video game, a car moves from the point (1, 2) to the point (3, 4). Which transformation describes this movement?

Accepted Answer

Translation

Answer

Rotation

Answer

Reflection

Question 21

When a shape undergoes a translation, what remains unchanged?

Accepted Answer

Size and shape

Answer

Orientation and position

Answer

Area and perimeter

Answer

Number of vertices

Question 22

What is the axis of rotation when a shape is rotated 90 degrees clockwise around a point?

Accepted Answer

Vertical line passing through the point

Answer

Horizontal line passing through the point

Answer

Diagonal line passing through the point

Answer

Any line passing through the point

Question 23

What is the image of the point (3, 5) after a reflection over the y-axis?

Accepted Answer

(-3, 5)

Answer

(3, -5)

Answer

(5, 3)

Answer

(-5, 3)

Question 24

What is the angle of rotation when a shape is rotated 180 degrees counterclockwise around a point?

Accepted Answer

180 degrees

Answer

30 degrees

Answer

60 degrees

Answer

90 degrees

Question 25

Which transformation can increase the area of a rectangle?

Accepted Answer

Dilation

Answer

Translation

Answer

Reflection

Answer

Rotation

Question 26

In architecture, translations are used to design buildings. Describe how a translation can be used in architectural design and explain how it helps to achieve the desired outcome.

Accepted Answer

Moving a floor plan to the right to create a larger living room

Answer

Rotating a building 90 degrees to face a different direction

Answer

Reflecting a building over a horizontal line to create a symmetrical design

Answer

Enlarging a building by increasing its dimensions

Question 27

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

Accepted Answer

Enlargement

Answer

Translation

Answer

Rotation

Answer

Reflection

Question 28

When you move a shape from one place to another without changing its size or shape, you are performing which type of transformation?

Accepted Answer

Translation

Answer

Rotation

Answer

Reflection

Answer

Dilation

Question 29

What is the result of reflecting a triangle over the y-axis?

Accepted Answer

The triangle is flipped vertically.

Answer

The triangle remains the same.

Answer

The triangle is flipped horizontally.

Answer

The triangle is rotated 180 degrees.

Question 30

When you rotate a shape counterclockwise around a fixed point, the shape...

Accepted Answer

Stays the same distance from the fixed point.

Answer

Moves away from the fixed point.

Answer

Moves towards the fixed point.

Answer

Flips over the fixed point.

Question 31

In art, rotations can create symmetrical designs. How does the angle of rotation impact the design?

Accepted Answer

The angle of rotation determines the number of repeats in the design

Answer

The angle of rotation has no effect on the design

Answer

A larger angle of rotation creates a less symmetrical design

Question 32

A rectangle is translated 5 units to the right and 3 units up. Which point will be on the new rectangle?

Accepted Answer

(7, 6)

Answer

(2, 5)

Answer

(10, 0)

Answer

(5, 3)

Question 33

A square with vertices A(1, 1), B(1, 3), C(3, 3), and D(3, 1) is translated 2 units to the right and 4 units up. Calculate the coordinates of the translated square.

Accepted Answer

A'(3, 5), B'(3, 7), C'(5, 7), D'(5, 5)

Answer

A'(3, 3), B'(3, 5), C'(5, 5), D'(5, 3)

Answer

A'(1, 5), B'(1, 7), C'(3, 7), D'(3, 5)

Answer

A'(5, 3), B'(5, 5), C'(7, 5), D'(7, 3)

Question 34

A triangle is rotated 120 degrees clockwise about its center. Which transformation would undo this rotation?

Accepted Answer

Rotation of 120 degrees counterclockwise about the center

Answer

Translation of 5 units to the left

Answer

Reflection over the x-axis

Question 35

Which of these shapes is NOT preserved under a reflection over the x-axis?

Accepted Answer

A circle

Answer

A square

Answer

A rectangle

Question 36

A triangle is moved 3 spaces to the right and 2 spaces down. What happens to the triangle's orientation (how it's pointing)?

Accepted Answer

The triangle's orientation stays the same.

Answer

The triangle rotates 90 degrees.

Answer

The triangle flips vertically.

Answer

The triangle flips horizontally.

Question 37

Which transformation lets you move a shape without changing its size or how it looks?

Accepted Answer

Translation

Answer

Reflection

Answer

Rotation

Question 38

A triangle has corners at (1, 2), (3, 1), and (2, 4). You flip this triangle over a vertical line. What are the new corner points?

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 39

A parallelogram is moved 2 spaces to the right and 3 spaces up. One of its corners is at (5, 2). What are the coordinates of that same corner after the move?

Accepted Answer

(7, 5)

Answer

(3, -1)

Answer

(7, 2)

Answer

(3, 5)

Question 40

A shape is flipped over the x-axis (like a mirror) and then moved 4 spaces to the right. Which of these would end up with the shape in the same final position?

Accepted Answer

Move the shape 4 spaces to the right, then flip it over the x-axis.

Answer

Spin the shape a full half-turn (180 degrees).

Answer

Flip the shape over the y-axis and then move it 4 spaces up.

Question 41

Which transformation moves a shape sideways or up and down without changing its size or shape?

Accepted Answer

Translation

Answer

Reflection

Answer

Rotation

Answer

Dilation

Question 42

When a figure is flipped over a line, what type of transformation occurs?

Accepted Answer

Reflection

Answer

Dilation

Answer

Translation

Answer

Rotation

Question 43

If a figure is turned 90 degrees clockwise, which property of the figure has changed?

Accepted Answer

Orientation

Answer

Size

Answer

Shape

Answer

Area

Question 44

What is the term for the point around which a figure turns?

Accepted Answer

Center of rotation

Answer

Origin

Answer

Midpoint

Answer

Pivot point

Question 45

Which transformation would not change the size or shape of a figure?

Accepted Answer

Translation

Answer

Reflection

Answer

Rotation

Answer

Dilation

Question 46

When a figure is reflected over the x-axis, which of its measurements remains the same?

Accepted Answer

Height

Answer

Area

Answer

Perimeter

Answer

Width

Question 47

Which of the following is not considered a type of geometric transformation?

Accepted Answer

Stretching

Answer

Reflection

Answer

Translation

Answer

Rotation

Question 48

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

Accepted Answer

Translation

Answer

Rotation

Answer

Reflection

Answer

Dilation

Question 49

When a figure is moved 3 units to the right, what happens to its x-coordinate?

Accepted Answer

Increases by 3

Answer

Stays the same

Answer

Decreases by 3

Answer

Multiplies by 3