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:TranslationsReflectionsRotationsDilations

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

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

The figure moved 6 units left and 4 units down

Blue-original. Red-image

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.

Ex #1 (continued)

Original Figure

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.

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…

OYOOn 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)

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

No reflection

Now you try…

OYOTell 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)

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)

Now that we have reflected the coordinates, we need to translate them according to the rule

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)

C)

B) 1 line of symmetry

No lines of symmetry

4 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

Green HW:13.4 and 13.5 Green WS A13.4 and 13.5 Green WS B

Blue HW:13.4 and 13.5 Blue WS