Question

Show that the parallel lines AB and CD are not
transformed onto parallel lines under the
tranformation matrix (T]
|1 0 1|
|0 1 2|
|0 0 1|
where
A[I 2], B[2 4], C[2 6] and D[3 8]​

Answer 1

Given :  transformation matrix (T]

|1 0 1|

|0 1 2|

|0 0 1|

parallel lines AB and CD

A[I 2], B[2 4], C[2 6] and D[3 8]​

To Find :

Solution:

A[I 2], B[2 4],

=> AB Equation

 y  - 2   =  (4 - 2)/(2 - 1) (x - 1)

 = y - 2 = 2x - 2

=> 2x = y

=> 2x - y   = 0  

CD

y - 6  = (8-6)/(3 - 2)  ( x - 2)

=> y - 6  = 2x  - 4

=> 2x - y + 2  = 0

AB  * [T]

$\left[\begin{array}{ccc}2&-1&0\end{array}\right] \left[\begin{array}{ccc}1&0&1\\0&1&2\\0&0&1\end{array}\right]$

$\left[\begin{array}{ccc}2&-1&0\end{array}\right]$

2x - y  + 0 = 0

=> 2x - y = 0

AB is same as after transformation

CD  * [T]

$\left[\begin{array}{ccc}2&-1&2\end{array}\right] \left[\begin{array}{ccc}1&0&1\\0&1&2\\0&0&1\end{array}\right]$

$\left[\begin{array}{ccc}2&-1&2\end{array}\right]$

2x - y  + 2 = 0

CD is same as after transformation

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