Geometry Transformations: Master the Art of Geometric Manipulation

Question 1

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

Accepted Answer

Enlargement

Answer

Translation

Answer

Rotation

Answer

Dilation

Question 2

Which of the following is not a type of transformation we have studied in this unit?

Accepted Answer

Enlargement

Answer

Translation

Answer

Reflection

Answer

Rotation

Question 3

A translation is a transformation that moves a figure:

Accepted Answer

Parallel to itself

Answer

Perpendicular to itself

Answer

Along a curved path

Question 4

A rotation is a transformation that turns a figure:

Accepted Answer

About a fixed point

Answer

Along a straight line

Answer

Without changing its size or shape

Answer

Around a curved path

Question 5

A reflection is a transformation that:

Accepted Answer

Flips a figure over a line

Answer

Enlarges or reduces a figure

Answer

Translates a figure parallel to itself

Answer

Rotates a figure around a point

Question 6

A dilation is a transformation that:

Accepted Answer

Enlarges or reduces a figure

Answer

Rotates a figure around a point

Answer

Flips a figure over a line

Answer

Translates a figure parallel to itself

Question 7

Which of the following transformations is not rigid?

Accepted Answer

Dilation

Answer

Rotation

Answer

Reflection

Answer

Translation

Question 8

Identify the transformation that does not preserve distances:

Accepted Answer

Dilation

Answer

Reflection

Answer

Translation

Answer

Rotation

Question 9

Classify the transformation defined by the rule: (x, y) -> (x + p, y - q).

Accepted Answer

Translation

Answer

Dilation

Answer

Rotation

Answer

Reflection

Question 10

Which characteristic defines a glide reflection?

Accepted Answer

It consists of a translation followed by a reflection.

Answer

It preserves area.

Answer

It has a single fixed point.

Question 11

Simplify a dilation with a scale factor of 3 followed by a dilation with a scale factor of 2:

Accepted Answer

Dilation with a scale factor of 6

Answer

Rotation and reflection

Answer

Composite dilation and translation

Answer

Dilation with a scale factor of 5

Question 12

State a necessary and sufficient condition for the congruence of two figures:

Accepted Answer

Corresponding sides and angles are equal.

Answer

They have the same area.

Answer

Corresponding angles are equal.

Answer

Corresponding sides are equal.

Question 13

A composite transformation involves performing:

Accepted Answer

Two or more transformations in sequence

Answer

Translation only

Answer

Reflection only

Answer

Dilation only

Question 14

A significant skill developed through studying transformations is:

Accepted Answer

Spatial reasoning

Answer

Trigonometric calculation

Answer

Algebraic manipulation

Answer

Statistical analysis

Question 15

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

Accepted Answer

Dilation

Answer

Rotation

Answer

Reflection

Answer

Translation

Question 16

Which of the following transformations always produces a similar (not congruent) figure?

Accepted Answer

Dilation

Answer

Rotation

Answer

Reflection

Answer

Translation

Question 17

Which of the following transformations has only one line of symmetry?

Accepted Answer

Reflection

Answer

Rotation

Answer

Glide reflection

Question 18

If line segment AB is translated by a translation (3, 2), what are the new coordinates of the image of point B if its original coordinates were (4, 5)?

Accepted Answer

(7, 7)

Answer

(4, 7)

Answer

(7, 4)

Answer

(1, 3)

Question 19

Which of the following transformations is NOT a rigid transformation?

Accepted Answer

Dilation

Answer

Rotation

Answer

Translation

Question 20

What is the dilation factor that produces an image that is half the size of the original figure?

Accepted Answer

1/2

Answer

2

Answer

4

Answer

-2

Question 21

Which of the following is NOT a property of congruence transformations?

Accepted Answer

They preserve neither distance nor angle measure

Answer

They preserve angle measure but not distance

Answer

They preserve shape and size

Answer

They preserve distance but not angle measure

Question 22

Which transformation always preserves the distance between points?

Accepted Answer

Translation

Answer

Dilation

Answer

Reflection

Answer

Rotation

Question 23

A transformation that maps a figure onto itself is called a(n):

Accepted Answer

Isometry

Answer

Symmetry

Answer

Congruence

Answer

Homothety

Question 24

Which transformation is NOT a rigid transformation (one that preserves shape and size)?

Accepted Answer

Dilation

Answer

Translation

Answer

Rotation

Answer

Reflection

Question 25

The transformation that maps a point (x, y) to (y, x) is a:

Accepted Answer

Reflection across the line y = x

Answer

Reflection across the line y = -x

Answer

Translation by (1, 1)

Answer

Rotation by 90 degrees

Question 26

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

Accepted Answer

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

Answer

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

Answer

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

Answer

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

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 rotated square?

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 28

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

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 29

A triangle with vertices at (2, 2), (4, 4), and (6, 2) is dilated by a scale factor of 2 with respect to the origin. What are the coordinates of the dilated triangle?

Accepted Answer

(4, 4), (8, 8), (12, 4)

Answer

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

Answer

(4, 2), (8, 4), (12, 2)

Answer

(2, 4), (4, 8), (6, 4)

Question 30

A figure is rotated 180 degrees about a point. How many times does the figure coincide with itself during this rotation?

Accepted Answer

2

Answer

3

Answer

1

Question 31

A regular hexagon is reflected across a line of symmetry. What is the order of rotational symmetry of the resulting image?

Accepted Answer

6

Answer

2

Answer

1

Answer

3

Question 32

A square is dilated by a scale factor of 1/2. What is the ratio of the perimeter of the image to the perimeter of the original square?

Accepted Answer

1:2

Answer

2:1

Answer

4:1

Answer

1:1

Question 33

Which of the following is NOT a rigid transformation?

Accepted Answer

Dilation

Answer

Reflection

Answer

Translation

Answer

Rotation

Question 34

Find the coordinates of the image of point (2, -3) after a translation of 3 units to the right and 2 units up.

Accepted Answer

(5, -1)

Answer

(5, 1)

Answer

(2, -5)

Answer

(2, 1)

Question 35

Which of the following is the correct formula for the rotation of point (x, y) clockwise around the origin by 90 degrees?

Accepted Answer

(-y, x)

Answer

(y, x)

Answer

(x, -y)

Answer

(x, y)

Question 36

A rectangle is reflected over the line y = x. Which of the following is the image of a vertex at (-2, 3)?

Accepted Answer

(3, -2)

Answer

(-3, -2)

Answer

(-2, -3)

Answer

(3, 2)

Question 37

What is the scale factor of a dilation that transforms a triangle with an area of 12 cm² into one with an area of 48 cm²?

Accepted Answer

2

Answer

3

Answer

4

Answer

6

Question 38

Which of the following transformations always preserves distance?

Accepted Answer

Translation

Answer

Rotation

Answer

Dilation

Question 39

Find the composite transformation of a reflection over the x-axis followed by a translation of 5 units to the right.

Accepted Answer

Translation of 5 units to the right followed by a reflection over the x-axis

Answer

Translation of 5 units to the left followed by a reflection over the x-axis

Answer

Reflection over the y-axis followed by a translation of 5 units to the right

Question 40

Which of the following shapes has only one line of symmetry?

Accepted Answer

Triangle

Answer

Circle

Answer

Square

Question 41

Two triangles are congruent if they have

Accepted Answer

The same three side lengths

Answer

The same two side lengths and one angle

Answer

The same area

Answer

The same three angles

Question 42

Which of the following is a property of a glide reflection?

Accepted Answer

It is a transformation that combines a reflection and a translation

Answer

It has a single fixed point

Answer

It always preserves orientation