1. ## Reflection of x=2

Need urgent help on this thanks.

A reflection in the line x=2 followed by a reflection in the x axis.

And also

a reflection in y=x followed by a reflection in the line y=-x

thank youuuuu

2. ## Re: Reflection of x=2

Do you want to find a matrix which represents these transformations on $\mathbb{R}^2$?

3. ## Re: Reflection of x=2

in the form (x,y) ---> (?x+?,?y+?)

4. ## Re: Reflection of x=2

In first case the reflection of point (x,y) in the line x = a will be
(x,y) -----> (( 2a - x ), y) and then in the x axis it will be ((2a-x) , -y )
Thus the reflection in both the lines ie., x=a and x axis taken together will be
(x,y) ----> ((2a-x), -y )

5. ## Re: Reflection of x=2

Originally Posted by alex123
Need urgent help on this thanks.

A reflection in the line x=2 followed by a reflection in the x axis.
The point (x, y) is distance x- 2 from the line x= 2. It will be mapped to the point that distance on the other side: 2- (x- 2)= 4- x. Reflecting (x, y) in the line x= 2 maps it to (4- x, y). Reflecting in the x-axis just changes the sign on y. "A reflection in the line x=2 followed by a reflection in the x axis" maps (x, y) to (4- x, -y).

And also

a reflection in y=x followed by a reflection in the line y=-x
A reflection in y= x maps (x, y) to (y, x). Why don't you think about "reflection in the line y= -x"? If you are not sure draw a graph.

thank youuuuu