Question

3. Find the matrix representing reflection in the line
4y - 3x = 0​

Answer 1

Answer:

2x3from 256442z3335gk

Answer 2

Given :   linear transformation of   reflection in the line 4y - 3x = 0​

To Find :  Matrix

Solution:

Matrix representation of  linear transformation of   reflection in the line  y = mx

is given by :

$A=\dfrac{1}{1+m^2} \left[\begin{array}{ccc}1-m^2&2m\\2m&m^2-1\end{array}\right]$

4y - 3x = 0

=> 4y = 3x

=> y = 3x/4

=> y = (3/4)x  

=> m = 3/4

1 + m²  = 1 + (3/4)²  =  25/16   => 1/(1 + m²)  = 16/25

1 - m² = 1 - (3/4)²  =  7/16

2m  =   2(3/4)  = 3/2

$A=\dfrac{16}{25} \left[\begin{array}{ccc}\frac{7}{16} &\frac{3}{2}\\\frac{3}{2}&-\frac{7}{16} \end{array}\right]$

$A=\dfrac{1}{25} \left[\begin{array}{ccc}7 &24\\24&-7 \end{array}\right]$

$A= \left[\begin{array}{ccc}\frac{7}{25} &\frac{24}{25}\\\frac{24}{25}&-\frac{7}{25} \end{array}\right]$

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