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Lesson 8.6, For use with pages 433-438
1. A
Give the coordinates of the point.
2. B
3. C
4. D
Lesson 8.6, For use with pages 433-438
ANSWER (–3, 2)
1. A
Give the coordinates of the point.
ANSWER (1, –3)
2. B
ANSWER (2, 2)
3. C
ANSWER (2, 0)
4. D
8.6 Reflections and Symmetry
Essential Questions
• What are the similarities and differences among transformations?
• How are the principles of transformational geometry used in art, architecture and fashion?
• What are the applications for transformations?
Transformational Geometry• Transformation: an operation that changes
a figure into another figure. The new figure created is called the image.
• For example: such as a slide, flip, or turn.
• Slide or translation
• Flip or rotation
Transformational Geometry• Reflection: a transformation that flips a
figure over a line and creates a mirror image of each point of a figure.
EXAMPLE 1 Identifying a Reflection
Tell whether the red figure is a reflection of the bluefigure.
a. b.
The figure is a reflection. The figure is not a reflection.
GUIDED PRACTICE for Examples 1 and 2
ANSWER no
1. Tell whether the red arrow is a reflection of the blue arrow.
EXAMPLE 2 Reflecting in the y-Axis
SOLUTION
Original ImageA(– 1, 1)B(– 3, 1)C(– 4, 3)D(– 2, 4)
A’(1, 1)B’(3, 1)C’(4, 3)D’(2, 4)
Quadrilateral ABCD is reflected in the y-axis. Write the coordinates of each vertex of quadrilateral ABCD and its image, quadrilateral A’B’C’D.
Transformation GeometryRule Sheet
• Do NOT lose this sheet.• You may put examples on it.• If you can keep track of it, you will be able to use it
on the test.• If you lose it, I will not give you another copy. You
will have to make your own copy by looking at someone else's sheet.
• PUT YOUR NAME ON IT!
Reflection
• To reflect across the x-axis
– Multiply the y coordinate by -1. (x, -y)
• To reflect across the y-axis
– Multiply the x coordinate by -1. (-x, y)
2. Graph the triangle with vertices J(0, 1), K(0, 4), and L(5,2). Reflect the triangle in the y-axis.
ANSWER
3. Graph the figure with vertices S(–3, 2), T(–1, 4), U(–4, 5), and V(–5, 3). Reflect the figure in the x-axis. Label the coordinates of the vertices of S’T’U’V’.
Original Image (– x, y)S(–3, 2)T(–1, 4)U(–4, 5)V(–5, 3)
(– x, –y)S’(–3, –2)T’(–1, –4)U’(–4, –5)V’(–5, –3)
ANSWER
GUIDED PRACTICE for Example 3
3. Graph the figure with vertices S(–3, 2), T(–1, 4), U(–4, 5), and V(–5, 3).Reflect the figure in the x-axis. Label the coordinates of the vertices of S’T’U’V’.
Original Image (– x, y)S(–3, 2)T(–1, 4)U(–4, 5)V(–5, 3)
(– x, –y)S’(–3, –2)T’(–1, –4)U’(–4, –5)V’(–5, –3)
EXAMPLE 3 Standardized Test Practice
SOLUTION
Original Image(x, y)P(1, 3)Q(4, 4)R(5, 2)
(x, –y)P’(1, –3)Q’(4, –4)R’(5, –2)
Reflect across the x-axis. Multiply each y-coordinate by – 1.
EXAMPLE 3 Standardized Test Practice
SOLUTION
Original Image(x, y)P(1, 3)Q(4, 4)R(5, 2)
(x, –y)P’(1, –3)Q’(4, –4)R’(5, –2)
Multiply each y-coordinate by – 1.
Transformational Geometry• Line of Symmetry: divides a figure into two
congruent parts that are mirror images of each other.
EXAMPLE 4 Identifying Lines of Symmetry
How many lines of symmetry does the picture have?
a. one line of symmetry
b. five lines of symmetry
c. no lines of symmetry
GUIDED PRACTICE for Example 4
1. How many lines of symmetry does a square have?
A square has 4 lines of symmetry.ANSWER
A rhombus has 2 lines of symmetry.
a rhombus?
ANSWER
Homework
• Worksheet 8.6
