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Example 9-5b Objective Identify figures with line symmetry and graph reflections on a coordinate plane

Example 9-5b Vocabulary Line symmetry Figures that match exactly when folded in half

Example 9-5b Vocabulary Lines of symmetry A line that divides a figure into two halves that are reflections of each other

Example 9-5b Vocabulary Reflections A type of transformation in which a figure is flipped over a line of symmetry

Lesson 9 Contents Example 1Identify Lines of Symmetry Example 2Identify Lines of Symmetry Example 3Identify Lines of Symmetry Example 4Reflect a Figure Over the x-axis Example 5Reflect a Figure Over the y-axis

Draw figure then determine whether the figure has line symmetry. If it does, draw all lines of symmetry. If it has no line symmetry, say “no symmetry” Example 9-1a Answer: Two lines of symmetry 1/5 Determine if there is a vertical line of symmetry Determine if there is a horizontal line of symmetry Determine if there is any diagonal lines of symmetry Yes No

Example 9-1b Answer: no symmetry 1/5 Draw figure then determine whether the figure has line symmetry. If it does, draw all lines of symmetry. If it has no line symmetry, say “no symmetry”

Example 9-2a Answer: One line of symmetry 2/5 Draw figure then determine whether the figure has line symmetry. If it does, draw all lines of symmetry. If it has no line symmetry, say “no symmetry” Determine if there is a vertical line of symmetry Yes Determine if there is a horizontal line of symmetry No Determine if there is any diagonal lines of symmetry No

Example 9-2b Answer: Two lines of symmetry. 2/5 Draw figure then determine whether the figure has line symmetry. If it does, draw all lines of symmetry. If it has no line symmetry, say “no symmetry”

Example 9-3a Answer: No line symmetry 3/5 Draw figure then determine whether the figure has line symmetry. If it does, draw all lines of symmetry. If it has no line symmetry, say “no symmetry” Determine if there is a vertical line of symmetry No Determine if there is a horizontal line of symmetry No Determine if there is any diagonal lines of symmetry No

Example 9-3b Answer: One line of symmetry 3/5 Draw figure then determine whether the figure has line symmetry. If it does, draw all lines of symmetry. If it has no line symmetry, say “no symmetry”

Example 9-4a Quadrilateral QRST has vertices Q(–1, 1), R(0, 3), S(3, 2), and T(4, 0). Find the coordinates of QRST after a reflection over the x-axis. Then graph both figures 4/5 Plot the 4 coordinates Q(-1, 1) R(0, 3) S(3, 2) T(4, 0) Label Q Label R Label S Label T Q R S T Connect the dots in order that was plotted

Example 9-4a Quadrilateral QRST has vertices Q(–1, 1), R(0, 3), S(3, 2), and T(4, 0). Find the coordinates of QRST after a reflection over the x-axis. Then graph both figures 4/5 Identify the line of reflection Q R S T x-axis

Example 9-4a Quadrilateral QRST has vertices Q(–1, 1), R(0, 3), S(3, 2), and T(4, 0). Find the coordinates of QRST after a reflection over the x-axis. Then graph both figures 4/5 Q R S T Copy reflection Begin with Q and count how far it is from the line of reflection (x-axis) It is 1 unit from the line of reflection Plot Q’ 1 unit on the other side of the line of reflection Label Q’ Q’

Example 9-4a Quadrilateral QRST has vertices Q(–1, 1), R(0, 3), S(3, 2), and T(4, 0). Find the coordinates of QRST after a reflection over the x-axis. Then graph both figures 4/5 Q R S T Begin with R and count how far it is from the line of reflection (x-axis) It is 3 units from the line of reflection Plot R’ 3 units on the other side of the line of reflection Label R’ Q’ R’

Example 9-4a Quadrilateral QRST has vertices Q(–1, 1), R(0, 3), S(3, 2), and T(4, 0). Find the coordinates of QRST after a reflection over the x-axis. Then graph both figures 4/5 Q R S T Begin with S and count how far it is from the line of reflection (x-axis) It is 2 units from the line of reflection Plot S’ 2 units on the other side of the line of reflection Label S’ Q’ R’ S’

Example 9-4a Quadrilateral QRST has vertices Q(–1, 1), R(0, 3), S(3, 2), and T(4, 0). Find the coordinates of QRST after a reflection over the x-axis. Then graph both figures 4/5 Q R S T Begin with T and count how far it is from the line of reflection (x-axis) It is 0 units from the line of reflection Plot T’ 0 units on the other side of the line of reflection Label T’ Q’ R’ S’ T’

Example 9-4a Quadrilateral QRST has vertices Q(–1, 1), R(0, 3), S(3, 2), and T(4, 0). Find the coordinates of QRST after a reflection over the x-axis. Then graph both figures 4/5 Q R S T Q’ R’ S’ T’ Connect the new lines in order Answer:

Quadrilateral ABCD has vertices A(–3, 2), B(–1, 5), C(3, 3), and D(2, 1). Find the coordinates of ABCD after a reflection over the x-axis. Then graph the figure and its reflected image. Answer: Example 9-4b 4/5

Example 9-5a Triangle XYZ has vertices X(1, 2), Y(2, 1), and Z(1, –2). Find the coordinates of XYZ after a reflection over the y-axis. Then graph the figure and its reflected image. 5/5 Plot the 3 coordinates X(1, 2) Y(2, 1) Z(1, -2) Label X Label Y Label Z X Y Z Connect the dots in order that was plotted

Example 9-5a Triangle XYZ has vertices X(1, 2), Y(2, 1), and Z(1, –2). Find the coordinates of XYZ after a reflection over the y-axis. Then graph the figure and its reflected image. 5/5 X Y Z Identify the line of reflection y-axis

Example 9-5a Triangle XYZ has vertices X(1, 2), Y(2, 1), and Z(1, –2). Find the coordinates of XYZ after a reflection over the y-axis. Then graph the figure and its reflected image. 5/5 X Y Z Copy reflection Begin with X and count how far it is from the line of reflection (y-axis) It is 1 unit from the line of reflection Plot X’ 1 unit on the other side of the line of reflection Label X’ X’

Example 9-5a Triangle XYZ has vertices X(1, 2), Y(2, 1), and Z(1, –2). Find the coordinates of XYZ after a reflection over the y-axis. Then graph the figure and its reflected image. 5/5 X Y Z Begin with Y and count how far it is from the line of reflection (y-axis) It is 2 units from the line of reflection Plot Y’ 2 units on the other side of the line of reflection Label Y’ X’ Y’

Example 9-5a Triangle XYZ has vertices X(1, 2), Y(2, 1), and Z(1, –2). Find the coordinates of XYZ after a reflection over the y-axis. Then graph the figure and its reflected image. 5/5 X Y Z Begin with Z and count how far it is from the line of reflection (y-axis) It is 1 unit from the line of reflection Plot Z’ 1 unit on the other side of the line of reflection Label Z’ X’ Y’ Z’

Example 9-5a Triangle XYZ has vertices X(1, 2), Y(2, 1), and Z(1, –2). Find the coordinates of XYZ after a reflection over the y-axis. Then graph the figure and its reflected image. 5/5 X Y Z X’ Y’ Z’ Connect the new lines in order Answer:

Example 9-5b Triangle QRS has vertices Q(3, 4), R(1, 0), and S(6, 2). Find the coordinates of QRS after a reflection over the y-axis. Then graph the figure and its reflected image. Answer: * 5/5

End of Lesson 9 Assignment Lesson 10:9Reflections All