15.6 Rotations in the Coordinate
Plane
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) What is the total amount of degrees in a circle?
2) Find the measure of the angles shown.
a)
b)
c)
Rotations in the Coordinate Plane
How do we rotate objects in the coordinate plane?
y
8
A
-8
A
-6
6
4
2
/
-4
-2
0
-2
-4
-6
-8
x
2
4
6
8
NOTES (2)
To rotate an object means to spin it around a single
point usually the origin.
Examples
Rotate A 90 degrees
counterclockwise around
the origin.
y
8
6
4
A/
2
-8
-6
-4
-2
0
2
-2
-4
-6
-8
A
4
6
x
8
EXAMPLES (3)
Rotate B 90 degrees counterclockwise around the
origin.
y
B
-6
6
4
B/
-8
8
2
-4
-2
0
-2
-4
-6
-8
x
2
4
6
8
NOTES (4)
x
-6
-6
-4
-8
-8
C
-2
-2
8
-8
6
-6
4
-4
2
-2
0
-4
-2
2
-4
4
-6
6
8
-8
0
y
2
2
4
6
8
x
We can get the coordinates of the image's vertices by
spinning our paper 90 degrees and imagining the new
coordinates.
y
Examples
Rotate C 90 degrees
8
counterclockwise around
6
the origin and find the new
4
vertices.
C
(−4,2) → ______
(−4, −2) → ______
(0,0) → ______
NOTES (5)
D
4
4
2
2
6
D/
8
8
y
6
x
Each vertex stays the exact same distance from the
point of rotation (the origin).
-6
-6
-4
-2
-2
-4
-8
8
-8
6
-6
4
-4
2
-2
0
-8
-2
2
-4
4
-6
6
8
-8
0
y
x
D
Examples
Rotate D 90 degrees
counterclockwise around
the origin and find the
coordinates of the new
vertices.
(2,0) → ______
(2, −2) → ______
(7, −2) → ______
NOTES (6)
For a 90 degree counterclockwise rotation:
(x, y) → ( − y,x)
y
HJKL is rotated 90 degrees
counterclockwise around
the origin. Find the
coordinates of the new
vertices.
8
6
L
4
H
2
-8
-6
-4
-2
0
-2
K -4
x
2
4
K
L
-6
J
-8
H
6
J
8
H(3, −6) → ______
J(0, −7) → ______
K (0, −4) → ______
L (3, − 5) → ______
EXAMPLES (7)
CDEF is rotated 90 degrees counterclockwise. Find
the coordinates of the new vertices.
y
8
6
4
C
2
-8
-6
-4
-2
0
2
F
-2
F
E
-4
C
-6
-8
4
D
D
6
8
E
x
C(1, −4) → ______
D(0,7) → ______
E(−2, −7) → ______
F(−1, − 4) → ______
EXAMPLES (8)
8
4
4
6
2
2
8
(1,3) → ______
(4, −2) → ______
x
-6
-6
-4
-2
-2
-4
-8
8
-8
6
-6
4
-4
2
-2
0
-8
-2
2
-4
4
-6
6
8
-8
0
y
Z
y
6
x
Rotate Z 90 degrees counterclockwise around the
origin.
(−4, −2) → ______
(−1,3) → ______
PRACTICE (9)
Rotate QR 90 degrees counterclockwise around the
origin and find the new endpoints.
y
Q (0,0) → ______
8
R (−6, −3) → _____
6
4
2
Q Q/
-8
R
-6
-4
-2
0
2
x
4
-2
-4
-6
-8
R/
6
8
PRACTICE (10)
Rotate ST 90 degrees counterclockwise around the
origin and find the new endpoints.
y
S(−2,2) → ______
T (−7,4) → ______
8
6
T
4
2
-8
-6
-4
S
-2 /0
S-2
-4
T/
-6
-8
x
2
4
6
8
FINAL QUESTION (11)
Yes or No. If DG is rotated 90 degrees counterclockwise
around the origin, is the length of DG changed?