Reflection MCC8.G.3 Describe the effect of dilations, translations, rotations and reflections on two-dimensional figures using coordinates. Picture with reflected caption (Basic) To reproduce the picture effects on this slide, do the following: On the Home tab, in the Slides group, click Layout and then click Blank. On the Insert tab, in the Images group, click Picture. In the Insert Picture dialog box, select a picture, and then click Insert. Under Picture Tools, on the Format tab, in the Size group, click the Size and Position dialog box launcher. In the Format Picture dialog box, resize or crop the image so that the height is set to 3.17” and the width is set to 10”. To crop the picture, click Crop in the left pane, and in the right pane, under Crop position, enter values into the Height, Width, Left, and Top boxes. To resize the picture, click Size in the left pane, and in the right pane, under Size and rotate, enter values into the Height and Width boxes. Select the picture. On the Home tab, in the Drawing group, click Arrange, point to Align, and then do the following: Click Align to Slide. Click Align Top. Under Picture Tools, on the Format tab, in the Picture Styles group, click Picture Effects, point to Reflections, and then under Reflection Variations click Half Reflection, touching (first row, second option from the left). On the Insert tab, in the Text group, click Text Box, and then on the slide, drag to draw the text box. Enter text in the text box, select the text, and then on the Home tab, in the Font group, select Impact from the Font list and then enter 42 in the Font Size box. On the Home tab, in the Paragraph group, click Align Text Right to align the text right in the text box. Select the text box. Under Drawing Tools, on the Format tab, in the WordArt Styles group, click Text Effects, point to Reflection, and then under Reflection Variations click Half Reflection, touching (first row, second option from the left). Under Drawing Tools, on the Format tab, in the WordArt Styles group, click the Format Text Effects dialog box launcher. In the Format Text Effects dialog box, click Text Fill in the left pane, select Solid fill in the Text Fill pane, and then do the following: Click the button next to Color, and then under Theme Colors, click White, Background 1 (first row, first option from the left). In the Transparency box, enter 12%. On the slide, drag the text box onto the picture to position as needed. To reproduce the background on this slide, do the following: Right-click the slide background area, and then click Format Background. In the Format Background dialog box, click Fill in the left pane, select Gradient fill in the Fill pane, and then do the following: In the Type list, select Radial. Click the button next to Direction, and then click From Center (third option from the left). Under Gradient stops, click Add or Remove until two stops appear on the slider. Also under Gradient stops, customize the gradient stops that you added as follows: Select Stop 1 from the list, and then do the following: In the Stop position box, enter 10%. Click the button next to Color, and then under Theme Colors click White, Background 1, Darker 5% (second row, first option from the left). Select Stop 2 from the list, and then do the following: In the Stop position box, enter 99%. Click the button next to Color, and then under Theme Colors click White, Background 1, Darker 35% (fifth row, first option from the left).

One type of transformation uses a line that acts like a mirror, with an image reflected across a line is a reflection and the mirror line is the line of reflection.

12.2 Reflection (flip) Example A 1. What are the coordinates for quadrilateral ABCD? Point A (1,1) Point B (2,3) Point C (4,4) Point D (5,2) 2. How far is each point from the line of reflection? Point A is 1 unit Point B is 2 units Point C is 4 units Point D is 5 units Quadrilateral ABCD is being reflected across the y-axis.

12.2 Reflection (flip) Example A 3. Using the information in question 2, how far should the image be from the line of reflection? Pre-image Point A is 1 unit Point B is 2 units Point C is 4 units Point D is 5 units Image Point A′ is 1unit Point B′ is 2 units Point C′ is 4 units Point D′ is 5 units Each vertex should be the same distance from the line of symmetry, just in the opposite position. REMEMBER:

12.2 Reflection (flip) Example A 4. What are coordinates for quadrilateral A’B’C’D’? A′ (-1,1) B′ (-2,3) C′ (-4,4) D′ (-5,2) 5. Compare and contrast the coordinates for original and the image? Pre-image A (1,1) B (2,3) C (4,4) D (5,2) Image A′ (-1,1) B′ (-2,3) C′ (-4,4) D′ (-5,2)

12.2 Reflection (flip) Example B Write down the coordinates for the original and the image. Compare and contrast the coordinates? Pre-Image F (2,3) G (4,1) H (1,0) Image F′ (2,-3) G′ (4,-1) H′ (1,0) This time the original is being reflected over the x-axis.

What to remember… When you reflect over the y-axis the x-coordinates change to its opposite and the y-coordinates stay the same. When you reflect over the x-axis the x-coordinates stay the same and the y-coordinates change to its opposite.

Reflection- the figure is flipped over a line. Reflection over the x-axis: (x, y) (x, -y) Reflection over the y-axis: (x, y) (-x, y)

What happens if the line of reflection is not the axis?

Reflections in other lines . . . Let’s look at what happens if you reflect a figure across the line y = x or line y = -x y = -x y = x Look at corresponding points. Notice that for (x, y), the corresponding image point is (y, x). For (-2, 5), image point is (5, -2). Look at corresponding points. Notice that for (x, y), the corresponding image point is (-y, -x). For (6, 3), image point is (-3, -6)

What does y=a look like? a represents any number. Let’s graph y = 3 What type of line did you graph? Horizontal line y = 3 x y (x,y) -2 3 (-2,3) 1 (1,3) 4 (4,3)

What does x=c look like? c represents any number. Let’s graph x = -2 What type of line did you graph? Vertical line x = -2 x y (x,y) -2 5 (-2,5) (-2,0) -3 (-2,-3)

Reflections in more lines . . . What happens if you reflect in a line y = 3? or x = -2 ? x = -2 B B’ y = 3 A A’ Each point and corresponding image must be equidistant from the line. Note A (4, 2) and image point A′(4, 4) are each 1 unit from the line y = 3. Each point and corresponding image must be equidistant from the line. Note B (0, 4) and image point B′(-4, 4) are 2 units from the line x = -2.

Steps to finding the image coordinates Determine if the figure will reflect horizontally or vertically. This will tell you which coordinate will change. Since it Y=3 only the y-coordinate will change. Find the distance between the pre-image coordinate and the line of reflection by subtracting the coordinate from the value of the line. U (-3, 5) 5 – 3 = 2 U is 2 units above y=3 So how far should U′ be the line of reflection? 2 units below

Steps to finding the image coordinates Since it should be below, subtract the distance from the value of the line of reflection. Check by graphing U (-3,5) U′ should be 2 units below Line of reflection y=3 3-2 = 1 So U′ should be at (-3,1)

Reteach Video next

Reflection Reflect ABC across the x-axis. Count the number of units point A is from the line of reflection. A Count the same number of units on the other side and plot point A’. B 3 Units Count the number of units point B is from the line of reflection. 4 Units C 1 Unit Count the same number of units on the other side and plot point B’. 1 Unit C’ 3 Units 4 Units Count the number of units point C is from the line of reflection. B’ Count the same number of units on the other side and plot point C’. A’

Reflections in a line Reflections can be made across the x-axis. Look at the corresponding points in the figures. The point (-4, 4) corresponds to the image point (-4, -4). The point (2, 4) corresponds to (2, -4). Notice that in a reflection over the x-axis, the coordinates of the x’s stay the same but the y’s change sign. In a reflection across the x-axis, the point (x, y) reflects onto image (x, -y).

Reflection Reflect ABC across the y-axis. Count the number of units point A is from the line of reflection. 5 Units 5 Units A A’ Count the same number of units on the other side and plot point A’. 2 Units 2 Units B B’ 3 Units 3 Units Count the number of units point B is from the line of reflection. C C’ Count the same number of units on the other side and plot point B’. Count the number of units point C is from the line of reflection. Count the same number of units on the other side and plot point C’.

Reflections in the y axis Reflections can be made across the y-axis. y-axis Check the corresponding points here. Notice that the point (2, 1) corresponds to (-2, 1). The point (7, 1) corresponds to (-7, 1). The y values stay the same, but the x values change sign. In a reflection across the y axis, the point (x, y) reflects onto image (-x, y).