10-9 reflections (page 456-459)

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10-9 Reflections (page 456- 459) Indicators G7-Identify the line & rotation symmetries of 2-d figures to solve problems. G8-Perform reflections of 2-d figures using a variety of methods.

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10-9 Reflections (page 456-459). Indicators  G7-Identify the line & rotation symmetries of 2-d figures to solve problems. G8-Perform reflections of 2-d figures using a variety of methods. Reflections…. Figures that match exactly when folded in half have line symmetry . - PowerPoint PPT Presentation

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Page 1: 10-9 Reflections (page 456-459)

10-9 Reflections (page 456-459)

Indicators G7-Identify the line & rotation symmetries

of 2-d figures to solve problems.G8-Perform reflections of 2-d figures using a variety of methods.

Page 2: 10-9 Reflections (page 456-459)

Reflections…

Figures that match exactly when folded in half have line symmetry.

Each fold line is called a line of symmetry. Some figures can be folded in more than one way to show symmetry.

Page 3: 10-9 Reflections (page 456-459)

You try…

• Determine whether each figure has line symmetry. If so how many? Where?

Page 4: 10-9 Reflections (page 456-459)

• A type of transformation where a figure is flipped over the line of symmetry is a reflection.

• Think of a mirror image. • As with translations, the original

figure and reflected image are congruent.

ReflectionReflection (flip)(flip)

Helpful Hints!Helpful Hints!

•When reflecting over the x-axis, change the When reflecting over the x-axis, change the y-coordinate to their opposites.y-coordinate to their opposites.

•When reflecting over the y-axis, change the When reflecting over the y-axis, change the x-coordinate to their opposites.x-coordinate to their opposites.

Page 5: 10-9 Reflections (page 456-459)

Example: Reflect a figure over the x-axis.

Quadrilateral QRST has vertices Q (-1,1),R (0,3), S (3,2), T (4,0).Find the coordinates of QRST after a reflection over the x-axis. Then graph the figure and its reflected image.

Q

RS

TQ’

R’S’

T’

The coordinates for the reflected image are Q (-1,-1), R (0,-3), S (3, -2), T (4,0). Check out the y-coordinates!

Page 6: 10-9 Reflections (page 456-459)

Example 2: Reflect a figure over the y-axis.

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

X

Y

Z

X1

Y1

Z1

The coordinates for the reflected image are X (-1,2), Y (-2,1), Z (-1,-2). Check out the x-coordinates!

Page 7: 10-9 Reflections (page 456-459)

Example 3: Reflect a figure over the x-axis.

Triangle XYZ has vertices X (1,2),Y (2,1), Z (1,-2). Find the coordinates of XYZ after a reflection over the x-axis. Then graph the figure and its reflected image.

X

Y

ZX’Y’

Z’

The coordinates for the reflected image are X (1,-2), Y (2,-1), Z (1,2). Check out the y-coordinates!

Page 8: 10-9 Reflections (page 456-459)

Homework

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