Name:________________________________________________________________ Date:__________________________ Period:______

Name:________________________________________________________________ Date:__________________________ Period:______

Name:________________________________________________________________
Date:__________________________ Period:______
Compositions
Do Now: Looking at the picture below, describe the type of rigid motion that takes place to go from:
________________________________________________
________________________________________________
When a series of rigid motions takes place with one rigid motion
building off another (as shown in the Do Now), this is called a ______________________________.
The symbol used for compositions is _________, which means _____________________
The notation rx-axis ◦ T3,4 is read as a reflection in the x-axis FOLLOWING a translation of (x+3,y+4). Basically, this
process is done in REVERSE. So whenever you see a composition of a transformation, you
work___________________________!!!
There are two different ways to write the composition listed in the Do Now:
1)
⃗⃗⃗⃗⃗⃗
2)
⃗⃗⃗⃗⃗⃗
Examples:
1) What is
Regents
̅̅̅̅
(
̅̅̅̅ (
))
on A(5,14)?
Common Core
2) What is (
(
(
))?
Graphing Example:
3) The coordinates of
are A(-2,2), B(-3,5) and C(-6,3). Graph and state the coordinates of
image of
after the composition
A composition of a translation and a reflection is called a _____________________________.
, the
More Examples:
4) Pentagon ABCDE is pictured to the right where and
compositions:
( )
a.
b.
(̅̅̅̅)
c.
( )
5) Using the diagram, write the rule of composition.
are lines of symmetry. Evaluate the following
6) Using the diagram, write the rule of composition.
7) In the diagram pictured below, what rigid motion(s) would map CD onto AB?
A
D
B
C
Name:________________________________________________________________
Compositions Homework
1) What is R-180˚ ◦ D2 on the point A(7,3)?
3) What is (
(
(
))?
Date:__________________________ Period:______
Geometry
2) What is
4) What is (
˚◦
(
(
)
(
on the point B(-2,8)?
))?
5) The coordinates of
are A(2,-1), B(5,-2) and C(3,-4). Graph and state the coordinates of
image of
after the composition
, the
6) The coordinates of
are A(-1,1), B(-5,3) and C(-2,7). Graph and state the coordinates of
image of
after the composition
, the
7) Hexagon ABCDEF is pictured to the right where and
compositions:
( )
a.
b.
(̅̅̅̅ )
c.
( )
8) Using the diagram, write the rule of composition.
are lines of symmetry. Evaluate the following
9) In the diagram pictured, all of the smaller
triangles are congruent to each other. What rigid
rigid motion(s) map ZB onto AZ?
A
X
Z
B
Review:
10) Review: Given
, construct the angle bisector. [Leave all construction marks.]
11) What is the slope of a line that is perpendicular to the line whose equation is 3x + 4y = 12?
(1)
(2)
(3)
(4)
Y
C