September 9, 2019
y
x
P
Warm up:Determine the coordinates of the image of P(4, -5) under each transformation. Plot and label each point:
1. A: Translation (x, y) ➔ (x – 3, y + 1) _______
2. B: Rotation of 90˚ clockwise about the origin ________
3. C: Reflection in x-axis ________
7a
September 9, 2019
1.6 Composition of Transformations
Learning Target:I can generate a composition of 2 or more transformations.
(G.Co.2, G.Co.3, G.Co.5)
September 9, 2019
2. Using ∆P'Q'R, reflect it in x-axis. Label this ∆P"Q"R"
y
x
P
Q R
TRY this:
3. What do you think this transformation is called?
___________ _____________________
1. Given ∆PQR, translate ∆PQR using (x, y) ➔ (x + 6, y – 2). Label this ∆ P'Q'R'.
tII r
Q R
P o
glide reflection
September 9, 2019
_______ ______________ is a special type of transformation in which a _________ is followed by a reflection. (Notice the notation!!)
Turn and talk: Do you think that the order you perform the transformations is important in a transformation that is the composition (combination) of transformations?
A
B
C
A'
B'
C' A"
B"
C"
first: glide
(translation)
second: reflection
glide reflectiontranslation
0
September 9, 2019
y
xE
D
Let's explore GLIDE REFLECTIONS:
1. The endpoints of DE are D(2, 1) and E(6, –1). DE is translated: (x, y) ➔ (x, y – 4) then reflect in the y-axis (Ry-axis). What are the coord. of the images?
D" (___, ___)
E" (___, ___)
D' (___, ___)
E' (___, ___)
2 3
6 5
D D 2 3w
E E b 5
September 9, 2019
Do you think that you will get the same thing if you reflect in the y-axis (Ry-axis) before you translate the points: (x, y) ➔ (x, y – 4)? Try it and see!
y
xE
D
D" (___, ___)
E" (___, ___)
D' (___, ___)
E' (___, ___)D
D Z 3
Lo 6 5
September 9, 2019
The glide reflection is an example of a composition of transformations.
A composition of transformations is when 2 or more transformations are combined to forma single transformation.
September 9, 2019
A B
C A' B'
C'
A"
B" C"
Problem Solving: How can we get from ∆ABC to ∆A"B"C" using a composition of transformations?
1st transformation: words: _____________________
notation:____________________
Describe the composition of transformations.
Hint: Watch notation!!!
2nd transformation: words: _____________________
notation:____________________
up2right
LCx.y 7Gt yt2rotate 98 do wa
oyRco 907
September 9, 2019
2. ∆RST has vertices R (1, 2), S (1, 4) and T (-3, 4). Rotate 90˚ clockwise about the origin: R(O, –90˚)(∆RST) and then
reflect it across the y-axis: Ry-axis. Graph each image & state coord.?
y
x
R
ST
R' (___, ___)
S' (___, ___)
T' (___, ___)
R" (___, ___)
S" (___, ___)
T" (___, ___)
L l
T T 4 I
4 3
rRft z i
y l
t 3
September 9, 2019
3: Sean reflects the parallelogram across the line p and then reflects the image across line q. Lines p and q are parallel and 5 cm apart. Describe a single transformation that moves the parallelogram from the original position to the final position.
p q5 cmn
September 9, 2019
Assignment:
Geo 1.6
Composition Worksheet
September 9, 2019
