15.7 Rotations – Day 2
Common Core Standards
8. G .1. Verify experimentally the properties of rotations, reflections, and
translations:
a. Lines are taken to lines, and line segments to line segments of the
same length.
b. Angles are taken to angles of the same measure.
c. Parallel lines are taken to parallel lines.
8.G. 2Understand that a two-dimensional figure is congruent to another if
the second can be obtained from the first by a sequence of rotations,
reflections, and translations; given two congruent figures, describe a
sequence that exhibits the congruence between them.
8. G.3 Describe the effect of dilations, translations, rotations, and
reflections on two-dimensional figures using coordinates.
8. G.4 Understand that a two-dimensional figure is similar to another if the
second can be obtained from the first by a sequence of rotations,
reflections, translations, and dilations; given two similar two-dimensional
figures, describe a sequence that exhibits the similarity between them.
WARM-UP (1)
1)  Rotate A 90 degrees counterclockwise around the
origin.
y
8
6
A
4
2
-8
-6
-4
-2
0
-2
-4
-6
-8
x
2
4
6
2) Find the measure of the
angles shown.
8
a)
b)
Rotations – Day 2
How do we rotate objects more than 90 degrees?
y
8
A
6
4
2
-8
-6
-4
A/
-2
0
-2
-4
-6
-8
x
2
4
6
8
NOTES (2)
Since there are 360 degrees in a circle, a rotation of 180
degrees is half way around. We can turn our paper
upside down to see the image.
y
2
4
6
-8
2
4
6
8
B
0
-6
-2
-4
-4
-2
-6
0
Examples
Rotate B 180 degrees
around the origin.
-8
8
y
8
6
4
2
-2
2
-2
-4
4
-4
-6
6
-6
-8
-8
B
8
x
x
NOTES (3)
For a 180 degree rotation direction doesn't matter –
clockwise and counterclockwise are the same.
y
0
2
4
-6
6
-8
-2
-4
-4
-2
-6
0
Rotate B 180 degrees
around the origin.
-8
2
-2
8
y
C
8
6
4
2
-2
4
-4
-4
6
-6
-6
-8
-8
8
2
4
6
8
C
x
x
NOTES (4)
In a rotation of 180 degrees each coordinate becomes
its opposite.
(x, y) → ( − x, − y)
y
8
H
Rotate HJKL180 degrees
around the origin.
J
6
L
4
K
2
-8
-6
-4
-2
0
x
2
4
-2
K -4
L
-6
J
-8
H
6
8
H(3, −6) → ______
J(0, −7) → ______
K (0, −4) → ______
L (3, − 5) → ______
EXAMPLES (5)
Rotate QR 180 degrees around the origin and find the
new endpoints.
y
Q (0,0) → ______
8
6
R (−6, −3) → _____
R/
4
/
Q Q
2
-8
R
-6
-4
-2
0
-2
-4
-6
-8
x
2
4
6
8
EXAMPLES (6)
Rotate D 180 degrees around the origin.
(1,3) → ______
(−1,3) → ______
y
(−4, −2) → ______
(4, − 2) → ______
8
6
4
D
-8
-6
2
-4
-2
0
x
2
4
6
8
-2
-4
-6
-8
Is the new image congruent
to the pre-image?
NOTES (7)
A 270 degree rotation is the same as a 90 degree
rotation the other way.
Rotate T 270 degrees
counterclockwise around
the origin.
y
T
8
6
4
2
-8
-6
-4
-2
0
-2
-4
-6
-8
x
2
4
6
8
Rotate T 90 degrees
clockwise around the
origin.
EXAMPLES (8)
Rotate QR 270 degrees counterclockwise around the
origin and find the new endpoints.
y
-8
Q (0,0) → ______
8
R
R/
-6
R (−6,3) → _____
6
-4
4
-8
-6
-4
-2
0
2
4
6
8
x
-8
-6
-4
-2
0
2
4
6
8
y
Q
-2
/
Q Q
2
2
-2
-4
4
R
6
-6
8
-8
x
EXAMPLES (9, 10)
Rotate UV 270 degrees counterclockwise around U.
U
V
U
V
PRACTICE (11)
Rotate U 180 degrees around the origin.
y
8
6
U
4
2
-8
-6
-4
-2
0
-2
-4
-6
-8
x
2
4
6
8
FINAL QUESTION (12)
Rotate QRST 270 degrees counterclockwise and
determine the new coordinates.
y
R
8
Q
6
4
2
-8
-6
-4
-2
S
0
-2
-4
-6
-8
T
Q
T
2
x
4
6
S
8
R
Q (−2,6) → ______
R (0,9) → ______
S(2,6) → ______
T (0,3) → ______