Lesson 17
NYS COMMON CORE MATHEMATICS CURRICULUM
M1
GEOMETRY
Name:___________________________________
Period:________ Date:_________
Lesson 17: Rotations on a Coordinate Plane
Warm Up
1. Use the rule (x, y)  (x + 4, y – 2) to find the translation image of LMN.
a. Graph the image as L’M’N’ and state the new coordinates.
b. State the rule in standard translation notation.
2. State the coordinates of ABC . Then, graph the image of ABC under the translation T1, 2 .
3. Write one translation rule that is equivalent to the composite transformation: T -3, 4 o T 2, -3.
Lesson 17
NYS COMMON CORE MATHEMATICS CURRICULUM
M1
GEOMETRY
Name:___________________________________
Period:________ Date:_________
Lesson 17: Rotations on a Coordinate Plane
Learning Targets
1. I can rotate a figure on the coordinate plane and draw the image
2. I can write down the rules of R90, R – 90 and R 180o
Rotations
A rotation is a transformation that turns a figure around a fixed point, called the center of rotation. A
rotation is an isometry, so the image of a rotated figure is congruent to the preimage.
Unless otherwise stated all rotations are counterclockwise. (Note, when you do not see a center of rotation,
you can assume that the center is the origin.)
Example 1. Rotate the figure with the given vertices.
M(5,8) N(8,4) P(10,10);
R90
M': ____________________________
N': ____________________________
P': _____________________________
Example 2. Draw DAN. D(4, 1) A(7, 3) N(5, 8)
State the coordinates of D’A’N’, the image of DAN after R90.
Original coordinates
Coordinates after R90.
Quick Write
Describe what happened to coordinates after a R90
around the origin?
Lesson 17
NYS COMMON CORE MATHEMATICS CURRICULUM
M1
GEOMETRY
Name:___________________________________
Period:________ Date:_________
Example 3. Draw DAN. D(4, 1) A(7, 3) N(5, 8)
State the coordinates of D’A’N’, the image of DAN after R -90.
Original coordinates
Coordinates after R-90.
1. State the rule for R90: (x, y)  (
,
)
2. State the rule for R-90 = R270: (x, y )  (
Example 4. Rotate the figure with the given vertices.
M(-5,2) N(-6,8) P(-12,12); R180
M': ____________________________
N': ____________________________
P': _____________________________
Quick Write
Describe what happened to coordinates after a R180 around the
origin?
3. State the rule for R180: (x, y) 
(
,
)
,
)
Lesson 17
NYS COMMON CORE MATHEMATICS CURRICULUM
M1
GEOMETRY
Name:___________________________________
Period:________ Date:_________
Lesson 17: Rotations on a Coordinate Plane
Classwork
Rotating every 90˚
(x,y)
Counter clockwise
(x,y)
R90˚
R-90˚
R180˚
R-180˚
R270˚
R-270˚
R360˚
R-360˚
Clockwise
Part 1. Draw PEG with coordinates P (3, -1), E(5, 7), G(9, 0) on the graph below.
1. State the coordinates of P’E’G’, the image of PEG
after R90. Plot P’E’G’ on the same graph.
Original coordinates
Coordinates after R90.
2. State the coordinates of P”E”G”, the image of PEG
after R -90. Plot P”E”G” on the same graph.
Original coordinates
Coordinates after R-90.
3. State the coordinates of P’’’E’’’G’’’, the image of
PEG after R180. Plot P’’’E’’’G’’’ on the same graph.
Original coordinates
Coordinates after R180.
4. State the rule for R180: (x, y )  (
,
)
Lesson 17
NYS COMMON CORE MATHEMATICS CURRICULUM
M1
GEOMETRY
Name:___________________________________
Period:________ Date:_________
Part 2. Write the transformed coordinates of (-2, 7) for each rotation listed in the table below.
(-2,7)
Counter clockwise
(-2,7)
R90˚
R-90˚
R180˚
R-180˚
R270˚
R-270˚
R360˚
R-360˚
Clockwise
Part 3 Fluency Check (Students take 5 minutes to compete using the rules or the table above)
1. If the letter is rotated 180 degrees, which is the resulting figure?
1)
2)
3)
4)
2. What are the coordinates of , the image of
, after a rotation of 180º about the origin?
1)
2)
3)
4)
3. If point
is rotated counterclockwise 90° about the origin, its image will be point
1)
2)
3)
4)
4. What are the coordinates of 𝑀’ , the image of 𝑀(2,4), after a counterclockwise rotation of 90
about the origin?
1)
2)
3)
4)
5. What is the image of point
under the rotation
about
the origin?
1)
2)
3)
4)
6. What are the coordinates of the image of
after a clockwise rotation of 90 about the origin?
7. What is the image of
under
? ________________________
Lesson 17
NYS COMMON CORE MATHEMATICS CURRICULUM
M1
GEOMETRY
Name:___________________________________
Period:________ Date:_________
Lesson 17: Rotations on a Coordinate Plane
Homework
1. The coordinates of the vertices of
are
,
, and
. Triangle
after a rotation of 90° about the origin. State the coordinates of the vertices of
the set of axes below is optional.]
is the image of
. [The use of
2. The coordinates of the vertices of
are
,
, and
. State the coordinates of
, the image of
after a rotation of 90º about the origin. [The use of the set of axes below is
optional.]
Lesson 17
NYS COMMON CORE MATHEMATICS CURRICULUM
M1
GEOMETRY
Name:___________________________________
Period:________ Date:_________
3. The accompanying diagram shows the starting position of the spinner on a board game.
How does this spinner appear after a 270° counterclockwise rotation about point P?
4.
1)
5.
2)
3)
4)
6.
7.
8.
9.
10.
4. What is the image of the point
5. What is the image of the point
6. The point
on rotation of 90° about the origin?
under a clockwise rotation of 90°
about the origin?
is rotated 180 about the origin in a clockwise direction. What are the coordinates of its image?
7. What is the image of
?