Symmetry and Dilations December 9, 2009

Objectives Understand and apply different types of symmetry, verbally and in writing Understand dilation

What is symmetry? A figure has symmetry if there is an isometry that maps the figure onto itself. A figure in the plane can have reflectional symmetry or line symmetry, if there is a reflection that maps the figure onto itself.

Types of symmetry Reflection – see previous slide Rotational – A figure has rotational symmetry if there is a rotation of 180° or less that maps the figure onto itself.

Check out the lines of symmetry

Check out the lines of symmetry

Check out the lines of symmetry

Does these have rotational symmetry? At how many degrees? Figure Does it have rotational symmetry? How many degrees? Scalene triangle Isosceles triangle Equilateral triangle Square Rhombus Rectangle Regular pentagon Regular hexagon

What is dilation? The last transformation we will investigate is called a dilation. The definition of dilation includes the term scale factor. The scale factor n describes the size change from the original figure to the image. A scale factor often includes the units of measure. A dilation maps a figure to a similar figure. A dilation is a similarity transformation

Find the scale factor

Find the scale factor

Reduction vs. enlargement Notice that in the first figure the image is larger than the preimage (and the scale factor is greater than 1). If this is the case, then the dilation is an enlargement. In the second figure the image is smaller than the preimage (and the scale factor is less than 1). This is an example of a reduction.

Finding the image of a point To find the image of a point in the coordinate plane under a dilation with center at the origin, you simply multiply the x-coordinate and the y-coordinate by the scale factor.

Find the image of A(3, 2) under a dilation with center at the origin and scale factor 3.

Find the image of DABC under a dilation centered at the origin with a scale factor of 3.