Vector Graphics Transformations: Interactive Learning Quizzes

Question 1

Which of the following matrices represents a scaling transformation that doubles the size of an object in both x and y directions?

Accepted Answer

[2 0 0; 0 2 0; 0 0 1]

Answer

[1 0 0; 0 2 0; 0 0 1]

Answer

[2 0 0; 0 0 2; 0 0 1]

Answer

[0 2 0; 0 2 0; 0 0 1]

Question 2

Which transformation is a combination of a rotation of 60 degrees and a translation of (5, -2)?

Accepted Answer

[cos(60) -sin(60) 5; sin(60) cos(60) -2; 0 0 1]

Answer

[cos(60) sin(60) 5; -sin(60) cos(60) -2; 0 0 1]

Answer

[sin(60) cos(60) 5; cos(60) -sin(60) -2; 0 0 1]

Answer

[sin(60) -cos(60) 5; -cos(60) -sin(60) -2; 0 0 1]

Question 3

Find the inverse of the scaling transformation [2 0 0; 0 3 0; 0 0 1].

Accepted Answer

[0.5 0 0; 0 0.33333 0; 0 0 1]

Answer

[2 0 0; 0 0.33333 0; 0 0 1]

Answer

[0.5 0 0; 0 3 0; 0 0 1]

Answer

[2 0 0; 0 3 0; 0 0 1]

Question 4

Represent the point (4, -3) using homogeneous coordinates.

Accepted Answer

[4 -3 1]

Answer

[4 -3 0]

Answer

[0 4 -3]

Answer

[4 0 -3]

Question 5

What is the effect of applying a shear transformation with a factor of 0.5 in the x direction?

Accepted Answer

Skewing in the negative y direction

Answer

Stretching in the x direction

Answer

Skewing in the positive y direction

Answer

No effect

Question 6

What is the result of applying a shearing transformation with a shear factor of 0.5 along the x-axis to a square?

Accepted Answer

The square becomes a parallelogram tilted to the right.

Answer

The square becomes a parallelogram tilted to the left.

Answer

The square becomes a rectangle stretched horizontally.

Answer

The square becomes a rectangle compressed horizontally.

Question 7

Which of the following transformation matrices represents a scaling by a factor of 2 in the x-direction and 3 in the y-direction?

Accepted Answer

[2, 0, 0; 0, 3, 0; 0, 0, 1]

Answer

[3, 0, 0; 0, 2, 0; 0, 0, 1]

Answer

[2, 0, 0; 0, 2, 0; 0, 0, 1]

Answer

[0, 3, 0; 0, 2, 0; 0, 0, 1]

Question 8

What is the inverse of a scaling transformation with a scale factor of k?

Accepted Answer

Scaling by 1/k

Answer

Scaling by -k

Answer

Scaling by k^2

Answer

Scaling by sqrt(k)

Question 9

Which transformation can be used to reflect a figure about the x-axis?

Accepted Answer

Scaling by -1 in the x-direction

Answer

Rotation by 180 degrees about the y-axis

Answer

Shearing by 1 along the y-axis

Answer

Translation by 1 unit in the negative y-direction

Question 10

What is the composite transformation that results from applying a rotation of 45 degrees about the origin followed by a translation by 2 units along the x-axis?

Accepted Answer

Rotation by 45 degrees and translation by 2 units along the x-axis

Answer

Translation by 2 units along the x-axis and rotation by 45 degrees

Answer

Rotation by 45 degrees about a point 2 units to the right of the origin

Answer

Translation by 2cos(45) units along the x-axis and 2sin(45) units along the y-axis, followed by rotation by 45 degrees

Question 11

What is the purpose of using homogeneous coordinates in vector graphics transformations?

Accepted Answer

To represent points at infinity

Answer

To simplify inverse transformations

Answer

To improve the efficiency of matrix multiplications

Answer

To reduce the number of transformations required

Question 12

Which of the following is NOT a valid homogeneous coordinate representation of a point?

Accepted Answer

[x, y, z]

Answer

[x, y, 0]

Answer

[x, y, 1]

Answer

[x, y, z, w]

Question 13

How does the sequence of transformations impact the final appearance of a vector graphic?

Accepted Answer

The sequence of transformations can lead to different visual outcomes.

Answer

The sequence of transformations has no effect on the final visual outcome.

Answer

The sequence of transformations only matters when applying rotation and scaling.

Answer

The sequence of transformations does not affect the final visual outcome.

Question 14

Which transformation matrix scales a vector graphic by a factor of (x, y)?

Accepted Answer

[[x, 0, 0], [0, y, 0], [0, 0, 1]]

Answer

[[y, 0, 0], [0, x, 0], [0, 0, 1]]

Answer

[[0, x, 0], [0, 0, y], [0, 0, 1]]

Answer

[[0, 0, x], [0, 0, y], [0, 0, 1]]

Question 15

Applying a rotation transformation around the z-axis by 90 degrees results in:

Accepted Answer

Counterclockwise rotation by 90 degrees

Answer

Reflection about the x-axis

Answer

Reflection about the y-axis

Answer

Clockwise rotation by 90 degrees

Question 16

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

Accepted Answer

Shear

Answer

Uniform scaling

Answer

Non-uniform scaling

Answer

Differential scaling

Question 17

A transformation that can create a diamond shape from a square is:

Accepted Answer

Shearing

Answer

Translation

Answer

Rotation

Answer

Reflection

Question 18

What is the determinant of a rotation matrix around the z-axis?

Accepted Answer

1

Answer

0

Answer

-1

Question 19

What is the effect of a shear transformation along the x-axis?

Accepted Answer

Skewing a shape in the y-direction

Answer

Enlarging or shrinking a shape

Answer

Rotating a shape around a fixed point

Question 20

Which of the following is NOT a type of vector graphics transformation?

Accepted Answer

Rasterization

Answer

Translation

Answer

Skewing

Question 21

How do you apply multiple transformations to a vector graphic in a specific order?

Accepted Answer

Multiply the transformation matrices in the desired sequence

Answer

Apply the transformations one after another, in any order

Answer

Create a new transformation matrix that combines all the individual transformations

Question 22

How do you find the inverse of a transformation matrix?

Accepted Answer

Use the adjoint matrix of the original matrix

Answer

Invert the individual elements of the matrix

Answer

Take the transpose of the matrix and divide by the determinant

Question 23

Which transformation matrix translates a point by (x, y)?

Accepted Answer

[1 0 0; 0 1 0; x 0 1]

Answer

[1 0 0; 0 1 0; 0 0 1]

Answer

[0 1 0; 0 1 0; x 0 1]

Answer

[0 0 1; 0 0 1; x y 1]

Question 24

A scaling transformation matrix with scale factors of 2 along both axes will:

Accepted Answer

Double the size of the object in both x and y directions.

Answer

Double the size of the object along the x-axis only.

Answer

Double the size of the object along the y-axis only.

Answer

Halve the size of the object in both directions.

Question 25

When applying multiple transformations to a point, the order in which they are applied matters.

Accepted Answer

True

Answer

False

Question 26

Which of the following is a homogeneous coordinate?

Accepted Answer

[x, y, 1]

Answer

[x]

Answer

[x, y]

Answer

[x, y, z, 1]

Question 27

What is the inverse of a translation transformation matrix?

Accepted Answer

A translation matrix with the opposite translation vector.

Answer

A translation matrix with the same translation vector.

Answer

A rotation matrix.

Answer

A scaling matrix.

Question 28

Which transformation matrix scales a point by (sx, sy)?

Accepted Answer

[[sx, 0, 0], [0, sy, 0], [0, 0, 1]]

Answer

[[sx, 0, 0], [0, 1, sy], [0, 0, 1]]

Answer

[[0, sx, 0], [sy, 0, 0], [0, 0, 1]]

Answer

[[1, sx, 0], [0, sy, 0], [0, 0, 1]]

Question 29

Determine the transformation matrix that rotates a point by an angle θ around the origin.

Accepted Answer

[[cos(θ), -sin(θ), 0], [sin(θ), cos(θ), 0], [0, 0, 1]]

Answer

[[cos(θ), 0, sin(θ)], [0, 1, 0], [0, 0, 1]]

Answer

[[sin(θ), cos(θ), 0], [cos(θ), -sin(θ), 0], [0, 0, 1]]

Answer

[[cos(θ), sin(θ), 0], [-sin(θ), cos(θ), 0], [0, 0, 1]]

Question 30

Construct the transformation matrix that applies a sequence of transformations in the order: translation, rotation, scaling.

Accepted Answer

[[cos(θ) * sx, -sin(θ) * sx, dx], [sin(θ) * sy, cos(θ) * sy, dy], [0, 0, 1]]

Answer

[[cos(θ) * sx, -sin(θ) * sy, dx], [sin(θ) * sx, cos(θ) * sy, dy], [0, 0, 1]]

Answer

[[cos(θ), -sin(θ), dx], [sin(θ), cos(θ), dy], [sx, sy, 1]]

Answer

[[sx, 0, dx], [0, sy, dy], [cos(θ), -sin(θ), 0]]

Question 31

What is the inverse operation of a translation transformation?

Accepted Answer

Translation by the negative of the translation vector

Answer

Translation by the translation vector

Answer

Rotation by 180 degrees

Question 32

Identify the transformation matrix that corresponds to a 45-degree clockwise rotation about the origin:

Accepted Answer

$$R_{45} =  egin{bmatrix} cos 45° & -sin 45°  sin 45° & cos 45°  end{bmatrix}$$

Answer

$$R_{90} =  egin{bmatrix} cos 90° & -sin 90°  sin 90° & cos 90°  end{bmatrix}$$

Answer

$$R_{-45} =  egin{bmatrix} -cos 45° & -sin 45°  sin 45° & -cos 45°  end{bmatrix}$$

Question 33

Which of the following transformations moves a vector by a specified distance along a given axis?

Accepted Answer

Translation

Answer

Scaling

Answer

Rotation

Answer

Shearing

Question 34

What is the homogeneous matrix representation of a scaling transformation with scale factors sx and sy?

Accepted Answer

[[sx, 0, 0], [0, sy, 0], [0, 0, 1]]

Answer

[[sy, 0, 0], [0, sx, 0], [0, 0, 1]]

Answer

[[sy, 0, 0], [0, sy, 0], [0, 0, 1]]

Answer

[[sx, 0, 0], [0, sx, 0], [0, 0, 1]]

Question 35

Which transformation can be used to create a reflection about a line passing through the origin?

Accepted Answer

Rotation by 180 degrees

Answer

Scaling

Answer

Translation

Answer

Shearing

Question 36

What is the effect of applying a translation transformation with a vector (dx, dy)?

Accepted Answer

Moves the vector dx units along the x-axis and dy units along the y-axis

Answer

Rotates the vector by dx degrees

Answer

Moves the vector dx units along the y-axis and dy units along the x-axis

Question 37

What is the inverse transformation of a rotation by an angle θ?

Accepted Answer

Rotation by -θ

Answer

Rotation by π - θ

Answer

Rotation by π + θ

Answer

Rotation by 2π - θ

Question 38

Which transformation can be used to distort a vector by stretching it in one direction while compressing it in another?

Accepted Answer

Shearing

Answer

Rotation

Answer

Scaling

Answer

Translation

Question 39

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

Accepted Answer

Translation

Answer

Shearing

Answer

Scaling

Answer

Rotation

Question 40

What is the result of applying a positive scale factor to a shape?

Accepted Answer

The shape becomes larger.

Answer

The shape becomes rotated.

Answer

The shape becomes tilted.

Answer

The shape becomes smaller.

Question 41

Which transformation involves rotating a shape around a specific point?

Accepted Answer

Rotation

Answer

Translation

Answer

Shearing

Answer

Scaling

Question 42

Which of the following is NOT a valid transformation matrix?

Accepted Answer

[0 1 0; 1 0 0; 0 0 0]

Answer

[1 0 0; 0 1 0; 0 0 1]

Answer

[2 0 0; 0 2 0; 0 0 1]

Answer

[cos(theta) -sin(theta) 0; sin(theta) cos(theta) 0; 0 0 1]

Question 43

What is the purpose of the identity matrix in vector graphics transformations?

Accepted Answer

To reset all transformations.

Answer

To shear a shape.

Answer

To scale a shape.

Answer

To translate a shape.

Question 44

What is the effect of applying the following transformation matrix to a shape: [cos(theta) -sin(theta) 0; sin(theta) cos(theta) 0; 0 0 1]?

Accepted Answer

Rotation about the origin by an angle theta.

Answer

Scaling by a factor of theta.

Answer

Translation by a distance theta.

Answer

Shearing by an angle theta.

Question 45

What is the purpose of using homogeneous coordinates in vector graphics transformations?

Accepted Answer

To allow for translations, projections, and 3D transformations.

Answer

To store additional data about the shape.

Answer

To represent colors and textures.

Answer

To improve the efficiency of calculations.

Question 46

Which transformation matrix scales a vector by a factor of 's' along the x-axis and 't' along the y-axis?

Accepted Answer

[[s, 0], [0, t]]

Answer

[[0, s], [t, 0]]

Answer

[[t, 0], [s, 0]]

Answer

[[s, t], [0, 0]]

Question 47

A triangle with vertices (0,0), (1,0), and (0,1) is rotated 90 degrees clockwise about the origin. What are the new coordinates of the vertex originally at (1,0)?

Accepted Answer

(0, -1)

Answer

(-1, 0)

Answer

(1, 1)

Answer

(0, 1)

Question 48

What is the result of applying a shear transformation with a shear factor of 2 along the x-axis to the point (3,4)?

Accepted Answer

(11, 4)

Answer

(3, 10)

Answer

(5, 6)

Question 49

Which transformation is not affine?

Accepted Answer

Perspective projection

Answer

Translation

Answer

Rotation

Question 50

What is the primary advantage of using homogeneous coordinates in vector graphics transformations?

Accepted Answer

Allows representation of translations as matrix multiplications.

Answer

Simplifies rotation calculations.

Answer

Reduces the number of operations needed for scaling.

Question 51

Which sequence of transformations is equivalent to first rotating a vector by angle 'θ' and then translating it by (tx, ty)?

Accepted Answer

Translate by (tx, ty) then rotate by 'θ'

Answer

Rotate by 'θ' then translate by (-tx, -ty)

Answer

The order of transformations doesn't matter.

Answer

Translate by (-tx, -ty) then rotate by 'θ'

Question 52

What is the inverse transformation of scaling by a factor of 'k'?

Accepted Answer

Scaling by a factor of '1/k'

Answer

Rotating by '1/k'

Answer

Translating by 'k'

Answer

There is no inverse for scaling.

Question 53

A transformation that preserves the parallelism of lines but not necessarily their lengths or angles is called?

Accepted Answer

Affine transformation

Answer

Similarity transformation

Answer

Euclidean transformation

Answer

Projective transformation

Question 54

What is the determinant of a transformation matrix that reflects a vector across the y-axis?

Accepted Answer

-1

Answer

0

Answer

1

Question 55

Which of the following is a common application of vector graphics transformations?

Accepted Answer

All of the above

Answer

Creating animations

Answer

Manipulating 3D models in graphic design software

Answer

Developing interactive user interfaces