1. ## Please check, Matrix transformation

A transformation f is a reflction in the line y = -x + 1

What I have done;

First I shifted the plane 1 unit down so that the line of reflection passes through the origin. I think the line y = -x makes an angle -45 degrees with the positive x - axis. It then follows that the reflection in this line is Q-45 degrees so that the required matrix is

Q-45 degrees ( Cos 270 Sin 270 ) = ( 0 -1 )
Sin270 -cos 270 -1 0

Then I find the reflection by using composite transformation
t 0,1 o (q -45 degrees 0 t 0,-1)

This gives f(x) = (0 -1)x + (1)
-1 0 1

A transformation f is a reflction in the line y = -x + 1

What I have done;

First I shifted the plane 1 unit down so that the line of reflection passes through the origin. I think the line y = -x makes an angle -45 degrees with the positive x - axis. It then follows that the reflection in this line is Q-45 degrees so that the required matrix is

Q-45 degrees ( Cos 270 Sin 270 ) = ( 0 -1 )
Sin270 -cos 270 -1 0

Then I find the reflection by using composite transformation
t 0,1 o (q -45 degrees 0 t 0,-1)

This gives f(x) = (0 -1)x + (1)
-1 0 1
This looks OK to me. (you can check this by finding the images of a three
points using a diagram, and checking the observation against the result
given by the transformation).

RonL

RonL