Transformations in Geometry: Master Translations, Rotations, and Reflections

Question 1

The transformation that moves a figure from one point to another without changing its orientation is called a:

Accepted Answer

Translation

Answer

Rotation

Answer

Reflection

Answer

Shear

Question 2

Which of the following transformations flips a figure over a line?

Accepted Answer

Reflection

Answer

Translation

Answer

Rotation

Answer

Dilation

Question 3

A transformation that turns a figure around a fixed point is called a:

Accepted Answer

Rotation

Answer

Translation

Answer

Reflection

Answer

Dilation

Question 4

What is the name of the fixed point around which a figure is rotated?

Accepted Answer

Center

Answer

Origin

Answer

Vertex

Answer

Intersection

Question 5

When a figure is translated (x, y) units, what happens to its coordinates?

Accepted Answer

They are added to (x, y)

Answer

They are multiplied by (x, y)

Answer

They are subtracted from (x, y)

Answer

They remain the same

Question 6

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

Accepted Answer

Preserves shape and size

Answer

Reverses orientation

Answer

Flips over a line

Answer

Has a fixed point

Question 7

What is the image of the point (3, 4) under a reflection over the y-axis?

Accepted Answer

(-3, 4)

Answer

(3, 4)

Answer

(4, 3)

Answer

(-4, 3)

Question 8

Triangle PQR has vertices P(1, 2), Q(3, 3), and R(2, 5). It is translated by the vector (3, -2). What are the coordinates of the translated point P'?

Accepted Answer

(4, 0)

Answer

(0, 0)

Answer

(3, 6)

Answer

(0, 2)

Question 9

Shape ABCD is rotated 90° clockwise about the origin (0, 0). Which of the following points will NOT move?

Accepted Answer

(0, 0)

Answer

(0, 2)

Answer

(2, 0)

Answer

(1, 1)

Question 10

What is the formula to translate a point (x, y) by a vector (a, b)?

Accepted Answer

(x + a, y + b)

Answer

(x - a, y - b)

Answer

(a - x, b - y)

Answer

(b - x, a - y)

Question 11

What is the image of the point (3, -5) under the dilation with a scale factor of 2 and center (1, 0)?

Accepted Answer

(6, -10)

Answer

(9, -5)

Answer

(3, -2.5)

Answer

(1, -5)

Question 12

A translation is a transformation that:

Accepted Answer

Moves a figure in a straight line without changing its size or orientation

Answer

Rotates a figure around a fixed point

Answer

Flips a figure over a line

Question 13

To rotate a figure 90 degrees clockwise around a fixed point, the angle of rotation is:

Accepted Answer

90 degrees

Answer

45 degrees

Answer

180 degrees

Answer

270 degrees

Question 14

When a figure is reflected over the x-axis, the y-coordinates of its points:

Accepted Answer

Change sign

Answer

Remain the same

Answer

Double

Answer

Halve

Question 15

A square undergoes two transformations: first, a 90-degree clockwise rotation about its center, followed by a translation by the vector (2, -1). What is the combined transformation?

Accepted Answer

Rotation by 90 degrees clockwise, followed by translation by (2, -1)

Answer

Translation by (2, 1), followed by rotation by 90 degrees clockwise

Answer

Translation by (2, -1), followed by rotation by 90 degrees counterclockwise

Answer

Reflection about the y-axis, followed by translation by (2, -1)

Question 16

Which transformation changes the size or shape of a figure?

Accepted Answer

Enlargement

Answer

Translation

Answer

Rotation

Answer

Reflection

Question 17

Which transformation does not alter the orientation of a shape?

Accepted Answer

Translation

Answer

Rotation

Answer

Reflection

Answer

Shear

Question 18

Which of the following lines is the line of reflection for the transformation that maps point A(2, 3) to point A'(5, 3)?

Accepted Answer

y = 3

Answer

x = 5

Answer

x = 2

Answer

y = 2

Question 19

A square is reflected over the x-axis. What is the relationship between the original square and its image?

Accepted Answer

Congruent and opposite in orientation

Answer

Similar and the same size

Answer

Congruent and the same orientation

Answer

Similar but different in size

Question 20

Which transformation will NOT preserve the size of a shape?

Accepted Answer

Dilation

Answer

Translation

Answer

Rotation

Answer

Reflection

Question 21

A point P(2, 5) is reflected over the line y = x. What are the coordinates of its image point?

Accepted Answer

(5, 2)

Answer

(2, 5)

Answer

(-2, 5)

Answer

(5, -2)

Question 22

Which of the following transformations moves a shape without modifying its size or orientation?

Accepted Answer

Translation

Answer

Rotation

Answer

Reflection

Question 23

Which transformation is NOT considered rigid?

Accepted Answer

Dilation

Answer

Translation

Answer

Rotation

Question 24

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

Accepted Answer

Stretching

Answer

Translation

Answer

Reflection

Answer

Rotation

Question 25

A translation is a transformation that:

Accepted Answer

Moves a shape from one position to another without altering its size or shape

Answer

Flips a shape over a line of symmetry

Answer

Rotates a shape around a specified point

Question 26

Which transformation does NOT preserve the original shape and size?

Accepted Answer

Enlargement

Answer

Translation

Answer

Rotation

Question 27

Which of the following is an example of a composite transformation?

Accepted Answer

A translation followed by a rotation

Answer

A single reflection

Answer

A single rotation

Answer

A single translation

Question 28

What is the inverse transformation of a 90-degree rotation about the point (0, 0)?

Accepted Answer

A 90-degree rotation in the opposite direction about the point (0, 0)

Answer

A translation of 90 units in the positive x-direction

Answer

A 90-degree rotation in the same direction about the point (0, 0)

Answer

A translation of 90 units in the negative x-direction

Question 29

Which transformation maps a shape onto itself without changing its size or shape?

Accepted Answer

Identity transformation

Answer

Translation

Answer

Rotation

Answer

Reflection

Question 30

A translation is a transformation that moves a shape:

Accepted Answer

In a straight line, without changing its size or shape

Answer

In a circular path, without changing its size or shape

Answer

In any direction, without changing its size or shape

Question 31

A rotation is a transformation that turns a shape:

Accepted Answer

Around a fixed point, without changing its size or shape

Answer

Around a fixed line, without changing its size or shape

Answer

In any direction, without changing its size or shape

Question 32

A reflection is a transformation that flips a shape:

Accepted Answer

Over a line, without changing its size or shape

Answer

In any direction, without changing its size or shape

Answer

Over a point, without changing its size or shape

Question 33

Which of the following is NOT a transformation?

Accepted Answer

Enlargement

Answer

Reflection

Answer

Translation

Answer

Rotation

Question 34

A composite transformation is a transformation that is:

Accepted Answer

Made up of two or more transformations applied in sequence

Answer

Applied to a shape in any order

Answer

Applied to a shape more than once

Question 35

The inverse of a transformation is a transformation that:

Accepted Answer

Undoes the original transformation

Answer

Is always the same as the original transformation

Answer

Can only be applied to translations

Answer

Is always different from the original transformation

Question 36

Which of the following transformations is a rigid transformation?

Accepted Answer

Rotation

Answer

Stretch

Answer

Enlargement

Answer

Shear

Question 37

A transformation that changes the size of a shape is called a:

Accepted Answer

Non-rigid transformation

Answer

Rigid transformation

Answer

Isometric transformation

Answer

Euclidean transformation

Question 38

Which of the following transformations is an example of a dilation?

Accepted Answer

Enlargement

Answer

Reflection

Answer

Translation

Answer

Shear

Question 39

Which of the following transformations will change the orientation of a figure?

Accepted Answer

Reflection

Answer

Dilation

Answer

Rotation

Answer

Translation

Question 40

Which of the following transformations will not change the coordinates of any point on the figure?

Accepted Answer

Identity transformation

Answer

Reflection over the y-axis

Answer

Rotation 90 degrees clockwise about the origin

Answer

Translation 1 unit right

Question 41

Which of the following is NOT an example of a rigid transformation?

Accepted Answer

Dilation

Answer

Reflection

Answer

Rotation

Answer

Translation

Question 42

A square has vertices at (1, 1), (3, 1), (3, 3), and (1, 3). The square is translated 2 units to the right and 1 unit down. What are the coordinates of the image of the vertex (1, 3) after the translation?

Accepted Answer

(3, 2)

Answer

(1, 2)

Answer

(1, 4)

Answer

(3, 4)

Question 43

A rectangle is rotated 90 degrees clockwise about its center. What is true about the image of the rectangle?

Accepted Answer

The image is congruent to the original rectangle.

Answer

The image is a reflection of the original rectangle.

Answer

The image is a different shape than the original rectangle.

Answer

The image is a dilation of the original rectangle.

Question 44

A circle has its center at (2, 3) and a radius of 5. The circle is translated 3 units to the left and 2 units up. What are the coordinates of the center of the image of the circle?

Accepted Answer

(-1, 5)

Answer

(5, 1)

Answer

(2, 1)

Answer

(5, 5)

Question 45

A line segment has its endpoints at (1, 2) and (4, 5). The line segment is translated 3 units to the left and 1 unit down. What is the length of the image of the line segment?

Accepted Answer

The same length as the original line segment.

Answer

1 unit shorter than the original line segment.

Answer

Cannot be determined without further information.

Answer

3 units longer than the original line segment.

Question 46

A parallelogram is reflected across a line. What is always true about the image of the parallelogram?

Accepted Answer

The image is congruent to the original parallelogram.

Answer

The image is a rotation of the original parallelogram.

Answer

The image is a different shape than the original parallelogram.