Chapter 3

Question 1

32 reflection rules

Answer 1

R(y=0) (x , -y)
R(x=0) (-x , y)
R(y=x) (y , x)
R(y=-x) (-y , -x)

Question 2

33 translation to reflection theorem

Answer 2

a translation is a composition at reflections across 2 parallel lines

Question 3

34 rotation to reflection theorem

Answer 3

any rotation can be expressed as a composition of reflections across 2 lines that can intersect at the center of rotation if the angle of rotation is twice the angle between the lines of reflection.

Question 4

35 the composition of 2 or more rigid motions is a rigid motion

Answer 4

the composition of 2 or more rigid motions is a rigid motion

Question 5

36 any rigid motion is either a ______,
_____,
_____,
or a _____.

Answer 5

any rigid motion is either a translation, reflection, rotation, or glide reflection

if M is a rigid motion, then:
M=R(l)
M=T<x,y>
M=r(n,P)
M=T<x,y> * R(l)

Question 6

37 corollary: any rigid motion can be expressed as a composition of reflections

Answer 6

if M is a rigid motion, then:
M=R(l)
M=R(l) * R(m)
M=R(l) * R(m) * R(n)