<p>What is the transformation matrix M that transforms a square in the x-y plane defined by (1, 1)<sup>T</sup> (-1, 1)<sup>T</sup> (-1, -1)<sup>T</sup> (1, -1)<sup>T</sup> to a parallelogram whose corresponding vertices are (2, 1)<sup>T</sup> (0,1)<sup>T</sup> (-2, -1)<sup>T</sup> and (0, -1)<sup>T</sup> ? Following are options below. This is not a homework question.</p>
<p><a href="https://i.sstatic.net/D7MuE.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/D7MuE.png" alt="enter image description here" /></a></p>
<p>I can easily find transformation matrix in 2X2 but how 3X3 ? I got confused between Option A and C. How third row and column is added ?</p>

CC BY-SA 4.0
2023-07-30T11:01:34.797Z
The 2x2 upper left matrix is a skew in both A and C, the third column adds a translation. In A the translation is 0,0 and in C the translation is 1,0.
pmw1234
CC BY-SA 4.0
2023-07-30T11:29:11.443Z
So, out of A and C, which one is correct ? and Why ?
Rajesh Prajapati
CC BY-SA 4.0
2023-07-30T12:16:36.207Z
I think the entire point of this question is to get the reader to recognize that a 2x2 matrix can be pulled out and multiplied by the points. Doing that to just 1 point will yield the correct answer since that point with either need to be translated(C) or left as is(A). I highly recommend going through the exercise of multiplying the 2x2 matrix by the first point to get the answer to the question.
pmw1234
<transformations><matrix><coordinates>
Computer Graphics Previous Year Question asked in UGC NET 2021
Rajesh Prajapati
# Computer Graphics Previous Year Question asked in UGC NET 2021

(Asked by: username_0 on 2023-07-30)

What is the transformation matrix M that transforms a square in the x-y plane defined by (1, 1)T (-1, 1)T (-1, -1)T (1, -1)T to a parallelogram whose corresponding vertices are (2, 1)T (0,1)T (-2, -1)T and (0, -1)T ? Following are options below. This is not a homework question.

[![enter image description here](https://i.sstatic.net/D7MuE.png)](https://i.sstatic.net/D7MuE.png)

I can easily find transformation matrix in 2X2 but how 3X3 ? I got confused between Option A and C. How third row and column is added ?

**Tags:** transformations, matrix, coordinates

> **Comments:**
> **username_1**: The 2x2 upper left matrix is a skew in both A and C, the third column adds a translation. In A the translation is 0,0 and in C the translation is 1,0.  
> **username_0**: So, out of A and C, which one is correct ? and Why ?  
> **username_1**: I think the entire point of this question is to get the reader to recognize that a 2x2 matrix can be pulled out and multiplied by the points. Doing that to just 1 point will yield the correct answer since that point with either need to be translated(C) or left as is(A). I highly recommend going through the exercise of multiplying the 2x2 matrix by the first point to get the answer to the question.  

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