Q.1 Which of the following is a basic 2D geometric transformation?
Translation
Reflection
Rotation
All of the above
Explanation - Translation, reflection, and rotation are all basic types of 2D geometric transformations.
Correct answer is: All of the above
Q.2 What is the result of applying a translation transformation to a point?
The point changes direction
The point moves to a new location
The point rotates around the origin
The point scales up
Explanation - Translation moves every point of an object by the same distance in a given direction.
Correct answer is: The point moves to a new location
Q.3 A rotation of 90° about the origin will map point (x, y) to which new coordinates?
(-y, x)
(y, -x)
(-x, -y)
(y, x)
Explanation - A counter-clockwise rotation of 90° about the origin maps (x, y) to (-y, x).
Correct answer is: (-y, x)
Q.4 What is the effect of scaling transformation on an object?
Changes size
Changes position
Changes color
Changes orientation
Explanation - Scaling increases or decreases the size of an object by a scale factor along x and y directions.
Correct answer is: Changes size
Q.5 Reflection about the x-axis maps point (x, y) to:
(x, -y)
(-x, y)
(-x, -y)
(y, x)
Explanation - Reflecting a point about the x-axis negates its y-coordinate.
Correct answer is: (x, -y)
Q.6 Which transformation preserves the shape and size of an object?
Scaling
Translation
Rotation
All of the above
Explanation - Rotation and translation are rigid transformations that preserve the shape and size, whereas scaling changes the size.
Correct answer is: Rotation
Q.7 What is the homogeneous coordinate representation of a 2D point (x, y)?
[x y 1]
[x y 0]
[x y z]
[x y 2]
Explanation - In homogeneous coordinates, a 2D point (x, y) is represented as [x y 1] to facilitate matrix transformations.
Correct answer is: [x y 1]
Q.8 Which of the following transformations is not linear in 2D?
Rotation
Translation
Scaling
Reflection
Explanation - Translation is not a linear transformation in the strict sense because it cannot be represented purely by a 2x2 matrix; it requires homogeneous coordinates.
Correct answer is: Translation
Q.9 A shear transformation changes:
Shape only
Size only
Position only
Orientation and shape
Explanation - Shearing slants the shape of an object along x or y direction, changing its orientation without affecting area.
Correct answer is: Orientation and shape
Q.10 If a point (3, 4) is scaled by 2 along both x and y axes, its new coordinates are:
(6, 8)
(3, 8)
(6, 4)
(1.5, 2)
Explanation - Scaling multiplies the coordinates by the scale factor along each axis: (x', y') = (sx*x, sy*y).
Correct answer is: (6, 8)
Q.11 Which of the following matrices represents reflection about the y-axis?
[[1, 0], [0, -1]]
[[-1, 0], [0, 1]]
[[0, 1], [1, 0]]
[[-1, 0], [0, -1]]
Explanation - Reflection about the y-axis negates the x-coordinate while keeping the y-coordinate unchanged.
Correct answer is: [[-1, 0], [0, 1]]
Q.12 Which of these transformations is used to move an object from one location to another?
Rotation
Translation
Scaling
Shear
Explanation - Translation shifts the object along x and y directions without changing its shape or orientation.
Correct answer is: Translation
Q.13 Rotation about an arbitrary point (h, k) can be achieved by:
Direct rotation matrix
Translation to origin, rotation, then translate back
Scaling followed by rotation
Reflection followed by rotation
Explanation - To rotate about a point other than the origin, we translate the point to the origin, rotate, and then translate back.
Correct answer is: Translation to origin, rotation, then translate back
Q.14 Which transformation type can produce a mirror image?
Translation
Rotation
Reflection
Scaling
Explanation - Reflection creates a mirror image of the object with respect to a specific line or axis.
Correct answer is: Reflection
Q.15 Combining two transformations in sequence is called:
Composite transformation
Inverse transformation
Rigid transformation
Affine transformation
Explanation - A composite transformation applies multiple transformations one after another.
Correct answer is: Composite transformation
Q.16 The determinant of a 2D rotation matrix is always:
0
1
-1
Depends on angle
Explanation - Rotation matrices are orthogonal with determinant 1, preserving area and orientation.
Correct answer is: 1
Q.17 Shearing along x-axis leaves which coordinate unchanged?
x-coordinate
y-coordinate
Both coordinates
None
Explanation - X-axis shearing changes the x-coordinate based on y but keeps y-coordinate constant.
Correct answer is: y-coordinate
Q.18 Uniform scaling means:
Scaling x and y by different factors
Scaling x and y by the same factor
Scaling only along x
Scaling only along y
Explanation - Uniform scaling maintains the shape by scaling both axes equally.
Correct answer is: Scaling x and y by the same factor
Q.19 Inverse of translation by (tx, ty) is:
Translation by (-tx, -ty)
Translation by (tx, -ty)
Translation by (-tx, ty)
Translation by (0,0)
Explanation - To undo a translation, move in the opposite direction by negating both x and y offsets.
Correct answer is: Translation by (-tx, -ty)
Q.20 What type of transformation is required to rotate an object about its center?
Scaling
Rotation
Translation
Reflection
Explanation - Rotation about the center changes the object's orientation while preserving shape and size.
Correct answer is: Rotation
Q.21 Reflection across y = x line maps (x, y) to:
(y, x)
(-x, y)
(-y, -x)
(x, -y)
Explanation - Reflection across y = x swaps the x and y coordinates.
Correct answer is: (y, x)
Q.22 Which transformation can change an object's area?
Translation
Scaling
Rotation
Reflection
Explanation - Scaling increases or decreases the size of the object, affecting its area.
Correct answer is: Scaling
Q.23 A point (x, y) after reflection about origin becomes:
(-x, -y)
(x, -y)
(-x, y)
(y, x)
Explanation - Reflection about origin negates both coordinates.
Correct answer is: (-x, -y)
Q.24 Translation matrices in homogeneous coordinates are of size:
2x2
2x3
3x3
4x4
Explanation - In homogeneous coordinates, 2D translation is represented using a 3x3 matrix.
Correct answer is: 3x3
Q.25 What is a characteristic of rigid transformations?
Preserve shape and size
Change shape
Change size
Shear the object
Explanation - Rigid transformations, like rotation and translation, preserve distances and angles, keeping shape and size unchanged.
Correct answer is: Preserve shape and size