Let be the line in the direction of the unit vector u through the point a (a) Write down the formula for the affine map defining the reflection through the line (b) Write down the formula for the glide reflection, as defined in Exercise 7 3 16, along by a distance d in the direction of u (c) Prove ...

a Fx Rx a a where R 2uu T I is the elementary reflection matrix corr ...

Let be the line in the direction of the unit vector u through the point a.

Question:

Let ℓ be the line in the direction of the unit vector u through the point a.
(a) Write down the formula for the affine map defining the reflection through the line ℓ.
(b) Write down the formula for the glide reflection, as defined in Exercise 7.3.16, along ℓ by a distance d in the direction of u.
(c) Prove that every improper affine plane isometry is either a reflection or a glide reflection.