Problem 1: Composing rotations.

Given the two points A and B below, let A_180 and B_60 be rotations with centers A and B by 180 and 60 degrees, respectively.  Let U = B_60 A_180.  Construct the geometrical defining data for U below, and also write exactly what transformation U is.

Problem 2: Transformations in the (x,y) plane

(a)    Point P = (0,0) and Q = (53, 102). Given the halfturns U = R_P and V = R_Q, what precisely is the transformation S = VUV? [Indicate the defining data.]

(b)   If line m is the set of (x,y) with x = 0 (i.e, the y-axis) what precisely is the transformation V  R_m? [Indicate the defining data.]

Problem 3.  Composing Reflections

In this figure, there is a point P and lines m and n.  Construct the point Q = R_mR_n(P).  Note:  No fair working outside the boundaries of the paper.

Problem 4.  Finding symmetries

Answer the question on the attached sheet with the pattern of squares.  NOTE.  If a line is BOTH the mirror line for a reflection and the invariant line for a glide reflection, just mark it as a mirror line.

Note for online version: This figure is not included. It is just a pattern of squares like graph paper (except that the squares were bigger). You can make your own by drawing a pattern of squares on graph paper.