Reflections and Symmetry 8-2 Reflections and Symmetry

Video Tutor Help Khan Academy Graphing reflections of a shape (8-2) Line of symmetry Reflection Dilation Translation Khan Academy Reflections and Symmetry Line of Reflection Graphing Reflections of a Shape Identifying Lines of Symmetry

Video Tutor Help Writing a rule to describe a translation Graphing translations Graphing reflections of a shape Finding the angle of rotation Graphing rotations Graphing dilation images

Worksheets Daily Notetaking Guide Worksheets Version A Lesson 8-2 Practice, Guided Problem Solving Practice 8-2 Guided Problem Solving 8-2

Vocabulary Practice Vocabulary (Electronic) Flash Cards Vocabulary 8A: Graphic Organizer Vocabulary 8B: Reading Comprehension Vocabulary 8C: Reading/Writing Math Symbols Vocabulary 8D: Visual Vocabulary Practice Vocabulary 8E: Vocabulary C Vocabulary 8F: Vocabulary Review Puzzle

Additional Lesson Examples Step-by-Step Examples Lesson 8-2

Lesson Readiness Problem of the Day Lesson 8-2 Lesson Quiz Lesson 8-2

Identify Line Symmetry TRILOBITES The trilobite is an animal that lived millions of year ago. Determine whether the figure has line symmetry. If it does, draw all lines of symmetry. If not, write none. Answer: This figure has one vertical line of symmetry. Example 6-1a

BOTANY Determine whether the leaf has line symmetry BOTANY Determine whether the leaf has line symmetry. If it does, draw all lines of symmetry. If not, write none. Answer: Example 6-1b

Identify Rotational Symmetry FLOWERS Determine whether the flower design has rotational symmetry. Write yes or no. If yes, name its angle(s) of rotation. Example 6-2a

Answer: Yes, this figure has rotational symmetry Answer: Yes, this figure has rotational symmetry. It will match itself after being rotated 90, 180, and 270. Example 6-2a

FLOWERS Determine whether the flower design has rotational symmetry FLOWERS Determine whether the flower design has rotational symmetry. Write yes or no. If yes, name its angle(s) of rotation. Answer: yes; 180 Example 6-2b

Identify Rotational Symmetry FLOWERS Determine whether the flower design has rotational symmetry. Write yes or no. If yes, name its angle(s) of rotation. Example 6-3a

Answer: Yes, this figure has rotational symmetry Answer: Yes, this figure has rotational symmetry. It will match itself after being rotated 60°, 120°, 180°, 240°, and 300°. Example 6-3a

FLOWERS Determine whether the flower design has rotational symmetry FLOWERS Determine whether the flower design has rotational symmetry. Write yes or no. If yes, name its angle(s) of rotation. Answer: no Example 6-3b

Draw a Reflection Copy trapezoid STUV below on graph paper. Then draw the image of the figure after a reflection over the given line. Example 7-1a

Step 1 Count the number of units between each vertex and the line of reflection. Answer: Step 2 Plot a point for each vertex the same distance away from the line on the other side. Step 3 Connect the new vertices to form the image of trapezoid STUV, trapezoid S'T'U'V'. Example 7-1a

Reflect a Figure over the x-axis Graph quadrilateral EFGH with vertices E(–4, 4), F(3, 3), G(4, 2) and H(–2, 1). Then graph the image of EFGH after a reflection over the x–axis and write the coordinates of its vertices. Example 7-2a

The coordinates of the vertices of the image are E'(–4, –4), F'(3, –3), G'(4, –2), and H'(–2, –1). Notice that the y–coordinate of a point reflected over the x–axis is the opposite of the y–coordinate of the original point. H(–2, 1) same opposites E(–4, 4) F(3, 3) G(4, 2) H'(–2, –1) G'(4, –2) F'(3, –3) E'(–4, –4) Example 7-2a

Answer: E'(–4, –4), F'(3, –3), G'(4, –2), and H'(–2, –1). Example 7-2a

Reflect a Figure over the y-axis Graph trapezoid ABCD with vertices A(1, 3), B(4, 0), C(3, –4), and D(1, –2). Then graph the image of ABCD after a reflection over the y–axis, and write the coordinates of its vertices. Example 7-3a

The coordinates of the vertices of the image are A'(–1, 3), B'(–4, 0), C'(–3, –4), and D'(–1, –2). Notice that the x–coordinate of a point reflected over the y–axis is the opposite of the x–coordinate of the original point. D(1, –2) opposites same A(1, 3) B(4, 0) C(3, –4) D'(–1, –2) C'(–3, –4) B'(–4, 0) A'(–1, 3) Example 7-3a

Answer: A'(–1, 3), B'(–4, 0), C'(–3, –4), and D'(–1, –2). Example 7-3a

Translation in a Coordinate Plane The vertices of ABC are A(–3, 7), B(–1, 0), and C(5, 5). Graph the triangle and the image of ABC after a translation 4 units right and 5 units down. This translation can be written as the ordered pair (4, –5). To find the coordinates of the translated image, add 4 to each x-coordinate and add –5 to each y-coordinate. translation 4 right, 5 down vertex A(1, 2)  (4, –5)  A(–3, 7) B(3, –5)  (4, –5)  B(–1, 0) C(9, 0)  (4, –5)  C(5, 5) Example 3-1a

The coordinates of the vertices of  ABC are A(1, 2), B(3, –5), and C(9, 0). Graph  ABC and  ABC. Answer: Example 3-1a

The vertices of DEF are D(–1, 5), E(–3, 1), and F(4, –4) The vertices of DEF are D(–1, 5), E(–3, 1), and F(4, –4). Graph the triangle and the image of DEF after a translation 3 units left and 2 units up. Answer: Example 3-1b

Reflection in a Coordinate Plane The vertices of a figure are M(–8, 6), N(5, 9), O(2, 1), and P(–10, 3). Graph the figure and the image of the figure after a reflection over the y-axis. To find the coordinates of the vertices of the image after a reflection over the y-axis, multiply the x-coordinate by –1 and use the same y-coordinate. reflection vertex M(8, 6)  M(–8, 6) N(–5, 9)  N(5, 9) O(–2, 1)  O(2, 1) P(10, 3)  P(–10, 3) Example 3-2a

The coordinates of the vertices of the reflected figure are M(8, 6), N(–5, 9), O(–2, 1) and P(10, 3). Graph the figure and its image. Answer: –8 –4 4 8 Example 3-2a

The vertices of a figure are Q(–2, 4), R(–3, 1), S(3, –2), and T(4, 3) The vertices of a figure are Q(–2, 4), R(–3, 1), S(3, –2), and T(4, 3). Graph the figure and the image of the figure after a reflection over the y-axis. Answer: Example 3-2b

To rotate the figure, multiply both coordinates of each point by –1. Rotations in a Coordinate Plane A figure has vertices A(–4, 5), B(–2, 4), C(–1, 2), D(–3, 1), and E(–5, 3). Graph the figure and the image of the figure after a rotation of 180°. To rotate the figure, multiply both coordinates of each point by –1. A(4, –5)  A(–4, 5) B(2, –4)  B(–2, 4) C(1, –2)  C(–1, 2) D(3, –1)  D(–3, 1) E(5, –3)  E(–5, 3) Example 3-3a

The coordinates of the vertices of the rotated figure are A(4, –5), B(2, –4), C(1, –2), D(3, –1), and E(5, –3). Graph the figure and its image. Answer: Example 3-3a

A figure has vertices A(2, –1), B(3, 4), C(–3, 4), D(–5, –1), and E(1, –4). Graph the figure and the image of the figure after a rotation of 180°. Answer: Example 3-3b

Reflections and Symmetry LESSON 8-2 Additional Examples Graph the point H (–4, 5). Then graph its image after it is reflected over the y-axis. Name the coordinates of H . Since H is 4 units to the left of the y-axis, The coordinates of H are (4,5). H is 4 units to the right of the y-axis.

Reflections and Symmetry LESSON 8-2 Additional Examples BCD has vertices B (–3, 1), C (–2, 5), and D (–5, 4). Graph BCD and its image after a reflection over the x-axis. Name the coordinates of the vertices of B C D . Reflect the other vertices. Draw B C D . Since B is 1 unit above the x-axis, B is 1 unit below the x-axis. The coordinates of the vertices are B (–3, –1), C (–2, –5), and D (–5, –4).

Reflections and Symmetry LESSON 8-2 Additional Examples Draw the lines of symmetry in the figure below. There is one line of symmetry.