# Geometry My great concern is not whether you have failed, but whether you are content with your failure. Abraham Lincoln Today:  Vocab Check Up  9.1/9.3.

## Presentation on theme: "Geometry My great concern is not whether you have failed, but whether you are content with your failure. Abraham Lincoln Today:  Vocab Check Up  9.1/9.3."— Presentation transcript:

Geometry My great concern is not whether you have failed, but whether you are content with your failure. Abraham Lincoln Today:  Vocab Check Up  9.1/9.3 Instruction  Practice

9.1/9.3: Reflections and Rotations Objectives: 1.Identify Reflections and Rotations 2.Use Reflections and Rotations on the coordinate plane Vocabulary:

CCSS 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 illustrated at the right. 2. Is the transformation isometric? 3. Name the transformation illustrated below. 4. Name the coordinate of each point: DG BE Vocab - Check

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

Graph Reflections: in a coordinate system. To graph a reflection: 1) If (x, y) is reflected in the x-axis, its image is the point (x, -y). 2) If (x, y) is reflected in the y-axis, its image is the point (-x, y).

Graph the given reflection. a) W (-3, 3) in y–axisb) AB in x-axis A B

Describe the transformation. 7.5 y x 0

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 Rotations: in a coordinate system.

Example 2: Graph the given points and rotation. Rotate the points A(5,-2) and B(-3, -2) 180° ccw (counterclockwise) about the 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.

Rotational Symmetry - when a figure can be mapped onto itself by a rotation of 180° or less. 90° rotation180° rotation

Rotational Symmetry - when a figure can be mapped onto itself by a rotation of 180° or less. no rotation180° rotation

Over Lesson 9–1 Example 3 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 5-Minute Check 2 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.

Example 3 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.

Example 5 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)

Geometry My great concern is not whether you have failed, but whether you are content with your failure. Abraham Lincoln Assignment:  9.1 p. 628 #25, 27, 29, 45, 47 AND 9.3 p. 643 # 3, 4, 37, 39, 40

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