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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
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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)
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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)