1. Warm up
Reflect the figure ABCD across the line y=x. List the new coordinates of the points A’B’C’D’.

2. Function Notation for Rotations
EQ: How can rotations be expressed through notation?
Assessment: Students will express notations through problems and a summary

3. Key Concept
A rotation is a transformation that turns a figure about a fixed point called the center of rotation. Rays drawn from the center of rotation to a point on its image form an angle of rotation.
An object and its rotation are the same size and shape, but the figure may be turned in different directions.
A positive angle of rotation turns the figure counter-clockwise and a negative angle of rotation turns the figure in a clockwise direction.

4. Rotating About The Origin
Rotation
Transformation EQ
90°
(x,y) → (-y, x)
180°
(x,y) → (-x, -y)
270°
(x,y) →(y, -x)

5. Example 1 Example triangle PQR has vertices P(1,1), Q(4, 5), R(5,1)
Graph ∆PQR and its image after a 90° rotation about the origin.

6. Example 2
Quadrilateral ACTS has vertices A(0,1), C(3, 4), T(-1,4) and S(-1,2). Graph ACTS and its image after a 270° rotation about the origin..

7. Example 3
Two rectangles are shown on the coordinate plane below. Hernando claims that the two rectangles are congruent. Which of the following statements could he use to prove his claim? Select all that apply.
A The rectangles are congruent since a translation of 6 units down and 7 units to the left carries Rectangle 1 onto Rectangle 2.
B The rectangles are congruent since a reflection over the x–axis followed by a translation of 7 units to the right carries Rectangle 1 onto Rectangle 2.
C The rectangles are congruent since a reflection over the y–axis followed by a translation of 1 unit to the right and 6 units up carries Rectangle 1 onto Rectangle 2.
D The rectangles are congruent since a rotation of 180° clockwise about the origin followed by a translation of 1 unit to the right carries Rectangle 1 onto Rectangle 2

8. Example 4
Rectangles 1 and 2 are drawn on a coordinate plane. Barry claims that the two rectangles are congruent. Which of the following sequences of rigid motions from Rectangle 1 to Rectangle 2 could Barry use to prove his claim? Select all that apply.
A Reflection over the x–axis, followed by a translation of 1 unit up.
B Translation of 1 unit up, followed by a translation of 6 units to the right.
C Rotation of 180° about the origin, followed by a translation of 4 units up.
D Translation of 6 units right and 4 units down, followed by a reflection over the x–axis.