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.

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Presentation transcript:

10-9 Reflections (page ) 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. Each fold line is called a line of symmetry. Some figures can be folded in more than one way to show symmetry.

You try… Determine whether each figure has line symmetry. If so how many? Where?

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. Reflection (flip) Helpful Hints! When reflecting over the x-axis, change the y- coordinate to their opposites.When reflecting over the x-axis, change the y- coordinate to their opposites. When reflecting over the y-axis, change the x- coordinate to their opposites.When reflecting over the y-axis, change the x- coordinate to their opposites.

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 R S T Q’ 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!

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 X1X1 Y1Y1 Z1Z1 The coordinates for the reflected image are X (-1,2), Y (-2,1), Z (-1,-2). Check out the x-coordinates!

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

Homework 10-8 pg #6-12 e, a10-8 pg #6-12 e, a 10-9 pg. 459 #16-27 a10-9 pg. 459 #16-27 a