GeometryGeometry

My great concern My great concern is not whether is not whether you have failed, you have failed, but whether you but whether you are content with are content with your failure.your failure.

Abraham LincolnAbraham Lincoln

Today:Today: Vocab Check UpVocab Check Up 9.1/9.3 9.1/9.3

InstructionInstruction PracticePractice

9.1/9.3: Reflections and Rotations

Objectives:1. Identify Reflections and Rotations2. Use Reflections and Rotations on the

coordinate plane

Vocabulary:

CCSSCCSS

Content Standards

G.CO.4 Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.

G.CO.5 Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another.

Mathematical Practices

5 Use appropriate tools strategically.

7 Look for and make use of structure.

1. Name the transformation 1. Name the transformation illustrated at the right.illustrated at the right.

2. Is the transformation isometric?2. Is the transformation isometric?

3. Name the transformation illustrated 3. Name the transformation illustrated below.below.

4. Name the coordinate of 4. Name the coordinate of each point:each point:

DD GG

BB EE

Vocab - CheckVocab - Check

Line of Symmetry – a line of reflection that reflects an object on to itself.

Line of Symmetry – a line of reflection that reflects an object on to itself.

Graph ReflectionsGraph Reflections: in a coordinate : in a coordinate system. system.

To graph a reflection:To graph a reflection:

1) If (x, y) is reflected in the x-axis, 1) If (x, y) is reflected in the x-axis, its image is the point (x, -y). its image is the point (x, -y).

2) If (x, y) is reflected in the y-axis, 2) If (x, y) is reflected in the y-axis, its image is the point (-x, y). its image is the point (-x, y).

Graph the given reflection.Graph the given reflection.

a) W (-3, 3) in y–axis b) AB in x-axis

A

B

Describe the transformation.

7.5

y

x0

1) 90° rotation – switch the x and y coordinates and change signs based on new quadrant

2) 180° rotation – change the signs of both the x and y coordinates.

Graph RotationsGraph Rotations: in a coordinate : in a coordinate system. system.

Example 2: Graph the given points and Example 2: Graph the given points and rotation.rotation.

Rotate the points A(5,-2) and B(-3, -2) Rotate the points A(5,-2) and B(-3, -2) 180° ccw (counterclockwise) about the 180° ccw (counterclockwise) about the origin.origin.

RST has coordinates R(-2, 3), S(0, 4), and T(3, 1). If RST is rotated 90° clockwise about the origin, what are the coordinates of the new vertices.

7.3

S(0,4)R(-2,3)

x

y

0

T(3,1)

R’(3,2)

T’(1,-3)

S’(4,0)

Example 3: Graph the given points and rotation.Example 3: Graph the given points and rotation.

Rotational Symmetry - when a figure can be mapped onto itself by a rotation of 180° or less.

90° rotation 180° rotation

Rotational Symmetry - when a figure can be mapped onto itself by a rotation of 180° or less.

no rotation 180° rotation

Over Lesson 9–1

A. (–5, –4)

B. (–5, 4)

C. (5, 4)

D. (4, –5)

Triangle PQR is shown below. What is the image of point Q after a 90° counterclockwise rotation about the origin?

Over Lesson 9–3

A. 180° clockwise

B. 270° clockwise

C. 90° clockwise

D. 90° counterclockwise

The coordinates of triangle XYZ before and after a rotation about the origin are shown in the table. Find the angle of rotation.

B. Quadrilateral WXYZ has vertices W(2, 4), X(3, 3), Y(2, 0), and Z(0, 2). Graph WXYZ and its image over y = –1.

A. B.

C. D.

Quadrilateral EFGH has vertices E(–3, 1), F(–1, 3), G(1, 2), and H(–3, –1). Graph EFGH and its image under reflection of the line y = x. Select the correct coordinates for the point H' in the new quadrilateral E'F'G'H'.A. E'(–3, –1), F'(–1, –3),

G'(1, –2), H'(–3, 1)

B. E'(3, –1), F'(1, –3), G'(–1, 2), H'(3, –1)

C. E'(1, –3), F'(3, –1), G'(2, 1), H'(–1, –3)

D. E'(–1, 3), F'(–3, 1), G'(–2, –1), H'(1, 3)

GeometryGeometry

My great concern My great concern is not whether is not whether you have failed, you have failed, but whether you but whether you are content with are content with your failure.your failure.

Abraham LincolnAbraham Lincoln

Assignment:Assignment: 9.1 p. 628 #25, 9.1 p. 628 #25,

27, 29, 45, 47 27, 29, 45, 47 ANDAND9.3 p. 643 # 3, 4, 9.3 p. 643 # 3, 4, 37, 39, 4037, 39, 40