Exercise 6.5.22

Answers

1.

Let

f (x) = x + t

be a translation. We may check it’s a rigid motion by

∥ f (x) - f (y) ∥ = ∥ (x + t) - (y + t) ∥ = ∥ x - y ∥ .

2.

Let

f, g

be two rigid motion, we have

∥ fg (x) - fg (y) ∥ = ∥ g (x) - g (y) ∥ = ∥ x - y ∥ .

So the composition of $f$ and $g$ is again a rigid motion.

jephianlin

2011-06-27 00:00