2011-25.md

course	course_year	question_number	tags	title	year
Geometry	IB	25	IB 2011 Geometry	Paper 3, Section I, F	2011

Let $R(x, \theta)$ denote anti-clockwise rotation of the Euclidean plane $\mathbb{R}^{2}$ through an angle $\theta$ about a point $x$.

Show that $R(x, \theta)$ is a composite of two reflexions.

Assume $\theta, \phi \in(0, \pi)$. Show that the composite $R(y, \phi) \cdot R(x, \theta)$ is also a rotation $R(z, \psi)$. Find $z$ and $\psi$.