13.4 and 13.5 Translations, reflections, and symmetry Pre-Algebra

Goal: Translate figures in a coordinate plane Reflect figures and identify lines of symmetry

Transformations Changes made to the location or to the size of a figure. Transformations include: Translations Reflections Rotations Dilations Think Transformers the movie.  The new figure formed by a transformation is called an image.

Translations Translations: Each point of a figure moves the same distance in the same direction. The figure does not change size or shape. Describe the translation in words The snow tuber moved 200 feet to the right and 40 feet down the hill. Tie this in with x value moved +200 and y valued moved -40. Blue is the original and red is the image

Describe the Translation in Words: The figure moved 4 units to the right and 3 units down Blue-original. Red-image The figure moved 6 units left and 4 units down 

Translating a Figure You can describe a translation of each point (x,y) of a figure using coordinate notation: a tells you how many units the point moves left or right b tells you how many units the point moves up or down

Translating a Figure Ex #1 Draw triangle ABC with vertices (corners) of A(3, -4), B(3,0), and C(5,2). Then find the coordinates of the vertices of the image after the translation (x,y)(x-6, y+2), and draw the image. Step 1-Plot the points and draw triangle ABC. Have small squares of graph paper ready. Walk them through plotting points as a reminder that you move side to side THEN up and down. (x,y)

Ex #1 (continued) Step 2-Rule: (x,y)(x-6, y+2) so we must subtract 6 from each x coordinate and add 2 to each y coordinate. Original Figure

Ex #1 (continued) Step 3-Draw triangle A’B’C’. (the apostrophe is read as A prime, B prime, C prime). Notice how each point moves 6 units to the left and 2 units up.

Now you try… OYO On graph paper… Translate the point J(-2, 4) using the rule: (x,y)(x+5, y-3). Name the new point J’ and state its coordinates. Translate the point S(4, 3) using the rule: (x,y)(x-4, y-1). Name the new point S’ and state its coodinates. J’ (3, 1) Solution: J’(3, 1) Solution: S’(0, 2) S’ (0, 2)

Tessellations Tessellation: A covering of a plane with a repeating pattern of one or more steps. There are no gaps or overlaps. Examples:

Creating Tessellations

Reflections and Symmetry Reflection-a transformation in which a figure is reflected or flipped over a line. Line of Reflection-the line that an image is flipped or reflected over. In this photo, the red line is a line of reflection. Where else have you seen lines of reflection?

Identifying Reflections Tell whether the transformation is a reflection. If so, identify the line of reflection. Reflection in x-axis Reflection in y-axis What type of transformation is the 3rd one-a TRANSLATION! ;) No reflection

Now you try… OYO Tell whether the transformation is a reflection. If so, identify the line of reflection. A) B) Solution: No reflection Solution: Reflection over the x-axis

Coordinate Notation To reflect in the x-axis, multiply the y-coordinate by -1. To reflect in the y-axis, multiply the x-coordinate by -1.

Reflecting a Polygon Because we are reflecting in the x-axis, we need to multiply our y-coordinates by -1 first. A(-6,2) becomes (-6,-2) B(-4,4) becomes (-4,-4) C(-2,2) becomes (-2,-2) D(-4,0) becomes (-4,0)

Reflecting a Polygon (continued) Now that we have reflected the coordinates, we need to translate them according to the rule A(-6,-2) becomes A’(-1, 3) B(-4,-4) becomes B’(1, 1) C(-2,-2) becomes C’(3, 3) D(-4,0) becomes D’(1, 5)

Line Symmetry Line Symmetry:When a figure is divided into two parts that are reflections of each other. Line OF Symmetry: the line that divides a figure into two parts.

Now you try… Tell how many lines of symmetry the figure has. A) B) 1 line of symmetry C) No lines of symmetry

Closure A transformation is when a figure moves location in a coordinate plane. A reflection is when a figure is reflected, or flipped over a line called the line of reflection. A figure has line symmetry if a line, called the line of symmetry, divides the figure into two parts that are reflections of each other.

Homework Blue HW: 13.4 and 13.5 Blue WS Green HW: 13.4 and 13.5 Green WS A 13.4 and 13.5 Green WS B Blue HW: 13.4 and 13.5 Blue WS