1

Objectives

• Define and draw lines of symmetry

• Define and draw dilations

2

Symmetry defined

• A figure has symmetry if there is a transformation such that the preimage and image coincide– Reflectional symmetry

– Rotational symmetry

3

Reflectional symmetry

• If there is a reflection that maps a figure onto itself, the figure has reflectional symmetry or line symmetry

• The figure may have one or more lines of symmetry, which divide the figure into two congruent halves

4

Rotational symmetry

• If there is a rotation of 180° or less that maps the figure onto itself, then the figure has rotational symmetry

• If the figure has 180° rotational symmetry, the figure has point symmetry

• Angle of rotation – how many degrees to rotate before figure is mapped onto itself

5

Angle of rotation

• Angle of rotation – smallest angle to rotate before figure is mapped onto itself

– 4 turns for one revolution

360° / 4 = 90°

– 3 turns for one revolution

360° / 3 = 120°

6

Dilation activity1. Plot and connect the following points on graph

paper A(-4, -4), B( -2, 6), C(4, 4) 2. Multiply the original coordinates by 2 and

plot/connect them on graph paper.3. Multiply the original coordinates by ½ and

plot/connect them on graph paper.4. Copy the original triangle onto patty paper.5. Compare corresponding angles of all three

triangles.6. Compare corresponding sides of all three

triangles in terms of lengths.

7

Dilation defined

• A dilation is a transformation that alters the size of the figure but does not change its shape– Similarity transformation– Not an isometry

8

Enlargement, reductionWhen both coordinates are

multiplied by the same number (scale factor), the size may change but the shape stays the same

• Enlargement – Scale factor greater than 1– Example: (x, y) (2x, 2y)

• Reduction – Scale factor between 0 and 1– Example: (x, y) (½ x , ½ y)

9

Distortion

• Multiplying each coordinate by a different number (or scale factor) – Example: horizontal stretching

• (x, y) (2x, y)

– Example: vertical shrinking

• (x, y) (x, ½ y)