# Computer Graphics Questions & Answers – Matrix Representations and Homogeneous Coordinates

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This section of our 1000+ Computer Graphics multiple choice questions focuses on Matrix Representations and Homogeneous Coordinates.

1.The matrix representation for translation in homogeneous coordinates is
a) P’=T+P
b) P’=S*P
c) P’=R*P
d) P’=T*P

Explanation: The matrix representation for translation is P’=T*P.

2. The matrix representation for scaling in homogeneous coordinates is
a) P’=S*P
b) P’=R*P
c) P’=dx+dy
d) P’=S*S

Explanation: The matrix representation for scaling is P’=S*P.

3. The matrix representation for rotation in homogeneous coordinates is
a) P’=T+P
b) P’=S*P
c) P’=R*P
d) P’=dx+dy

Explanation: The matrix representation for rotation is P’=R*P.

4. What is the use of homogeneous coordinates and matrix representation?
a) To treat all 3 transformations in a consistent way
b) To scale
c) To rotate
d) To shear the object

Explanation: To treat all 3 transformations in a consistent way, we use homogeneous coordinates and matrix representation.
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5. If point are expressed in homogeneous coordinates then the pair of (x, y) is represented as
a) (x’, y’, z’)
b) (x, y, z)
c) (x’, y’, w’)
d) (x’, y’, w)

Explanation: If point are expressed in homogeneous coordinates then we add 3rd coordinate to the point (x, y), that is represented as (x’, y’, w).

6. For 2D transformation the value of third coordinate i.e. w=?
a) 1
b) 0
c) -1
d) Any value

Explanation: For 2D we have (x, y, 1) i.e. w=1.

7. We can combine the multiplicative and translational terms for 2D into a single matrix representation by expanding
a) 2 by 2 matrix into 4*4 matrix
b) 2 by 2 matrix into 3*3
c) 3 by 3 matrix into 2 by 2
d) Only c

Explanation: We can combine the multiplicative and translational terms for 2D into a single matrix representation by expanding 2 by 2 matrix representation into 3 by 3.

8. The general homogeneous coordinate representation can also be written as
a) (h.x, h.y, h.z)
b) (h.x, h.y, h)
c) (x, y, h.z)
d) (x,y,z)

Explanation: The general homogeneous coordinate representation can also be written as (h.x, h.y, h).

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