# Computer Graphics Questions & Answers – Composite 2D Transformations

This set of Computer Graphics Questions and Answers for Aptitude test focuses on “Composite 2D Transformations”.

1. Two successive translations are___________________
a) Multiplicative
b) Inverse
c) Subtractive

P’= T(tx1, ty1) .[T(tx2, ty2)] P
= {T(tx1, ty1). T(tx2, ty2)}.P
Or T(tx1, ty1). T(tx2, ty2) = T(tx1+tx2 , ty1 + ty2).

2. Two successive translations are not commutative.
a) True
b) False

Explanation: According to commutative property, the order does not matter. Same as in the case of successive translations. Hence we can say that two successive translations are commutative.

3. General pivot point rotation can be expressed as _____________________
a) T(zr,yr).R(θ).T(-zr,-yr) = R(xr,yr,θ)
b) T(xr,yr).R(θ).T(-xr,-yr) = R(xr,yr,θ)
c) T(xr,yr).R(θ).T(-xr,-yr) = R(zr,yr,θ)
d) T(xr,yr).R(θ).T(-xr,-yr) = R(xr,yr,Q)

Explanation: Since the first two parameters are in 2D, hence only ‘x’ and ‘y’ can be variable along with ‘θ’. In other options, there is one more parameter ‘z’.

4. Which of the following is NOT correct? (A, B and C are matrices)
a) A.B = B.A
b) A.B.C = (A.B).C = A.(B.C)
c) C(A+B) = C.A + C.B
d) 1 A = A 1

Explanation: Matrix multiplication does not commute. We cannot switch the order of the factors and expect to end up with the same result. Hence, A.B ≠ B.A.

5. Reflection about the line y=0, the axis, is accomplished with the transformation matrix with how many elements as ‘0’?
a) 8
b) 9
c) 4
d) 6

Explanation: The matrix used for reflection about y=0 is an identity matrix with 6 ‘0’s and two ‘1’s and one element as ‘-1’.
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6. Which transformation distorts the shape of an object such that the transformed shape appears as if the object were composed of internal layers that had been caused to slide over each other?
a) Rotation
b) Scaling up
c) Scaling down
d) Shearing

Explanation: Two common shearing transformations are the type of transformation that shift coordinate x values coordinate y values. In shear transformation, the transformed shape appears as if the object were composed of internal layers that had been caused to slide over each other.

7. Transpose of a column matrix is________________
a) Zero matrix
b) Identity matrix
c) Row matrix
d) Diagonal matrix

Explanation: Transpose of a matrix is a matrix which is made by interchanging the rows and columns of the original matrix. Hence the transpose of column matrix is row matrix and vice versa.

8. Reversing the order in which a sequence of transformations is performed may affect the transformed position of an object.
a) True
b) False

Explanation: As we know that, matrix transformations are not commutative and the order of transformation matters. So it will affect the position of the object.

9. Which one of the following is the correct notation of a matrix with ‘m’ rows and ’n’ columns?
a) m + n
b) m – n
c) m x n
d) m/n

Explanation: m x n represents a matrix with ‘m’ number of rows and ‘n’ number of columns, while others are just arithmetic operations which can be done on 2 matrices.

10. How many minimum numbers of zeros are there in ‘3 x 3’ triangular matrix?
a) 4
b) 3
c) 5
d) 6

Explanation: In a triangular matrix, all entries, either above or below the diagonal are zero. So in case of ‘3 x 3’ matrix, there should be minimum 3 elements as 0.

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