Transformations in Geometry: Master Translations, Rotations, and Reflections

Question 1

What is the inverse of a translation of (3, -2)?

Accepted Answer

Translation (-3, 2)

Answer

Translation (3, 2)

Answer

Translation (-3, -2)

Answer

Translation (2, 3)

Question 2

Which transformation will change a circle into an ellipse?

Accepted Answer

Dilation

Answer

Translation

Answer

Rotation

Answer

Reflection

Question 3

What is the order of rotational symmetry for a regular hexagon?

Accepted Answer

6

Answer

2

Answer

3

Answer

4

Question 4

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

Accepted Answer

Enlargement

Answer

Translation

Answer

Rotation

Answer

Reflection

Question 5

A translation that moves a figure 5 units to the right is represented by:

Accepted Answer

T(5, 0)

Answer

T(-5, 0)

Answer

T(0, 5)

Answer

T(0, -5)

Question 6

What is the reflection of point (2, 3) across the y-axis?

Accepted Answer

(-2, 3)

Answer

(2, 3)

Answer

(3, 2)

Answer

(-3, 2)

Question 7

Which line is the line of reflection for the transformation y = -x?

Accepted Answer

y = -x

Answer

y = x

Answer

x = 0

Answer

y = 0

Question 8

Which point is invariant under a rotation of 180° about the origin?

Accepted Answer

(0, 0)

Answer

(1, 2)

Answer

(-1, 2)

Answer

(2, 1)

Question 9

Which of the following is NOT a type of transformation in geometry?

Accepted Answer

Resizing

Answer

Translation

Answer

Rotation

Answer

Reflection

Question 10

When performing a translation, in which direction(s) can a shape move?

Accepted Answer

Both horizontally and vertically

Answer

Horizontally only

Answer

Vertically only

Answer

Diagonally only

Question 11

What is the angle of rotation for a half-turn?

Accepted Answer

180°

Answer

90°

Answer

270°

Answer

360°

Question 12

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

Accepted Answer

Expansion

Answer

Translation

Answer

Rotation

Answer

Reflection

Question 13

A shape is translated 4 units to the right and 2 units down. What are the coordinates of its image if the original coordinates were (3, 5)?

Accepted Answer

(7, 3)

Answer

(7, 7)

Answer

(3, 7)

Answer

(1, 3)

Question 14

A shape is rotated 90 degrees clockwise about the origin. Which of the following transformations will undo this rotation?

Accepted Answer

Rotation 90 degrees anticlockwise about the origin

Answer

Rotation 180 degrees clockwise about the origin

Answer

Translation 5 units to the right

Answer

Reflection in the y-axis

Question 15

A parallelogram with vertices at (0, 1), (2, 1), (4, 3), and (2, 3) is translated 3 units to the right and 2 units up. What are the coordinates of the translated parallelogram?

Accepted Answer

(3, 3), (5, 3), (7, 5), (5, 5)

Answer

(0, 3), (2, 3), (4, 5), (2, 5)

Answer

(3, -1), (5, -1), (7, 1), (5, 1)

Answer

(0, -1), (2, -1), (4, 1), (2, 1)

Question 16

Which of the following transformations is NOT a rigid transformation?

Accepted Answer

Enlargement

Answer

Translation

Answer

Rotation

Answer

Reflection

Question 17

A circle with a radius of 5 cm is reflected over the x-axis. What will be the radius of the new circle?

Accepted Answer

5 cm

Answer

10 cm

Answer

25 cm

Answer

50 cm

Question 18

A triangle with vertices (2, 3), (4, 5), and (6, 3) is rotated 180 degrees around the origin. Which of the following represents the coordinates of the rotated triangle?

Accepted Answer

(-2, -3), (-4, -5), (-6, -3)

Answer

(-2, 3), (-4, 5), (-6, 3)

Answer

(2, -3), (4, -5), (6, -3)

Answer

(2, 3), (4, 5), (6, 3)

Question 19

Provide the rule for translating a shape with coordinates (x, y) by 5 units to the right.

Accepted Answer

(x + 5, y)

Answer

(x - 5, y)

Answer

(x, y + 5)

Answer

(x, y - 5)

Question 20

A shape is moved 4 units left and 2 units up. Which translation vector describes this transformation?

Accepted Answer

(-4, 2)

Answer

(4, -2)

Answer

(-4, -2)

Answer

(4, 2)

Question 21

What is the angle of rotation for a quarter turn anticlockwise around a fixed point?

Accepted Answer

90 degrees

Answer

180 degrees

Answer

270 degrees

Answer

360 degrees

Question 22

Identify the line of symmetry for a reflection that maps the point (1, 3) to the point (3, 3).

Accepted Answer

x = 3

Answer

y = x

Answer

y = -x

Answer

y = 3

Question 23

Which transformation can move a shape horizontally or vertically without changing its size or orientation?

Accepted Answer

Translation

Answer

Rotation

Answer

Reflection

Answer

Dilation

Question 24

Which type of symmetry is present in a rectangle?

Accepted Answer

Both horizontal and vertical

Answer

Horizontal only

Answer

Vertical only

Answer

Neither horizontal nor vertical

Question 25

A shape 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 26

Which transformation flips a shape over a line?

Accepted Answer

Reflection

Answer

Translation

Answer

Rotation

Answer

Dilation

Question 27

A shape is rotated 180 degrees about the origin. How does this transformation affect the shape's orientation?

Accepted Answer

It will be upside down.

Answer

It will be sideways.

Answer

It will be mirrored.

Answer

It will not change.

Question 28

Which of the following is NOT a characteristic of a translation?

Accepted Answer

Changes orientation

Answer

Maintains distance

Answer

Maintains angles

Answer

Maintains area

Question 29

Which transformation changes the size of a figure?

Accepted Answer

Dilation

Answer

Translation

Answer

Rotation

Answer

Reflection

Question 30

What is the angle of rotation for a 90-degree clockwise turn?

Accepted Answer

90°

Answer

45°

Answer

180°

Answer

270°

Question 31

When reflecting a shape over the y-axis, which point remains unchanged?

Accepted Answer

(3, 0)

Answer

(1, 2)

Answer

(4, -5)

Answer

(-2, 3)

Question 32

What type of transformation involves moving a figure along a straight line without altering its size or shape?

Accepted Answer

Translation

Answer

Rotation

Answer

Reflection

Answer

Shear

Question 33

A triangle is rotated 180° around the point (0, 0). What is its new orientation?

Accepted Answer

Inverted

Answer

Upright

Answer

Sideways

Answer

Rotated 45°

Question 34

A shape is translated by the vector (a, b). If the original coordinates were (x, y), what will be the new coordinates of the shape?

Accepted Answer

(x + a, y + b)

Answer

(x - a, y - b)

Answer

(x * a, y * b)

Answer

(x / a, y / b)

Question 35

A translation moves a shape:

Accepted Answer

Along a straight line

Answer

Around a fixed point

Answer

On a curved path

Answer

Randomly

Question 36

In a rotation, the fixed point about which the shape moves is called the:

Accepted Answer

Centre of rotation

Answer

Axis of rotation

Answer

Pivot point

Answer

Origin

Question 37

In the context of rotation, an angle measured in an anticlockwise direction is considered:

Accepted Answer

Positive

Answer

Negative

Answer

Neutral

Answer

Undefined

Question 38

During a reflection, a shape is flipped over a line known as the:

Accepted Answer

Mirror line

Answer

Symmetry line

Answer

Perpendicular line

Answer

Parallel line

Question 39

What is a composite transformation?

Accepted Answer

A combination of two or more transformations

Answer

A transformation that includes only translations

Answer

A transformation that includes only rotations

Answer

A transformation that includes only reflections

Question 40

Which of the following is NOT a rigid transformation?

Accepted Answer

Enlargement

Answer

Translation

Answer

Rotation

Answer

Reflection

Question 41

When reflecting a shape over the y-axis, what happens to its x-coordinate?

Accepted Answer

Changes sign

Answer

Stays the same

Answer

Is multiplied by -1

Answer

Is divided by -1

Question 42

Which transformation is represented by the following: (x + 4, y)?

Accepted Answer

A translation of 4 units to the right

Answer

A translation of 4 units to the left

Answer

A translation of 4 units up

Answer

A translation of 4 units down

Question 43

What is the name of the transformation where a shape is flipped over a line?

Accepted Answer

Reflection

Answer

Translation

Answer

Rotation

Answer

Enlargement

Question 44

What is the correct notation for a reflection over the y-axis?

Accepted Answer

R(y-axis)

Answer

R(x-axis)

Answer

R(origin)

Answer

R(x=0)

Question 45

The point (3, -2) is translated by the vector (2, 5). What are the coordinates of the translated point?

Accepted Answer

(5, 3)

Answer

(1, 3)

Answer

(5, -2)

Answer

(1, -2)

Question 46

What do we call a transformation involving a combination of two or more transformations?

Accepted Answer

Composite transformation

Answer

Single transformation

Answer

Inverse transformation

Answer

Identity transformation

Question 47

Which regular polygon has rotational symmetry of order 6?

Accepted Answer

Hexagon

Answer

Square

Answer

Pentagon

Answer

Octagon

Question 48

What is the point called around which a shape rotates?

Accepted Answer

Center of rotation

Answer

Origin

Answer

Vertex

Answer

Midpoint

Question 49

Which transformation does NOT preserve the size and shape of a figure?

Accepted Answer

Dilation

Answer

Translation

Answer

Rotation

Answer

Reflection

Question 50

A transformation that moves a shape without changing its size or shape is called an:

Accepted Answer

Isometry

Answer

Similarity

Answer

Congruence

Answer

Dilation

Question 51

What is the rule for translating a point (x, y) by 3 units to the right and 2 units up?

Accepted Answer

(x + 3, y + 2)

Answer

(x - 3, y + 2)

Answer

(x + 3, y - 2)

Answer

(x - 3, y - 2)

Question 52

What is the center of rotation for a 90-degree clockwise rotation of a shape about the origin?

Accepted Answer

(0, 0)

Answer

(1, 0)

Answer

(0, 1)

Answer

(1, 1)

Question 53

Which of the following is a composite transformation involving a translation and a reflection?

Accepted Answer

Glide reflection

Answer

Rotation

Answer

Dilation

Answer

Translation