12.1 – reflections 12.5 – symmetry m217 – geometry
TRANSCRIPT
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12.1 – Reflections12.5 – Symmetry
M217 – Geometry
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ISOMETRY
A movement or “translation” of a figure that preserves its original dimensions. Reflections Translations Rotations
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CC
Reflection – A transformation that uses a line that acts like a
mirror. Reflection
Line of Reflection
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Reflection Properties: Over y-axis(x, y) → ( )A (-2, 4)
B (2, -1)
C (0, 4)
D (-3, 0)
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Reflection Properties: Over x-axis(x, y) → ( )A (-2, 4)
B (2, -1)
C (0, 4)
D (-3, 0)
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Reflection Properties: Over y=x(x, y) → ( )A (3, 4)
B (1, 1)
C (-3, 2)
D (-32, 11)
y = x
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Ex: Reflection in the line y=1
y = 1
A (-1, 3)
B (3, -2)
C (0, 1)
D (-2, 0)
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Ex: Reflection in the line x = -2
x = -2
Triangle ABC: A (-1, 3) B (-3, -2) C (-4, 1)
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The Line of Symmetry is the imaginary line where you could fold an image and have both halves match
exactly.
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The Line of Symmetry is the imaginary line where you could fold an image and have both halves match
exactly.
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Determine the number of lines of symmetry in each logo
1.
2.
3.
4.
5.
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How many does the Mercedes logo have?
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How many does the Star of David have?
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Rotational Symmetry : if a figure can be mapped onto itself by a rotation of 180o or
less
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rotational symmetry : if a figure can be mapped onto itself by a rotation of 180o or
less
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rotational symmetry : if a figure can be mapped onto itself by a rotation of 180o or
less
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rotational symmetry : if a figure can be mapped onto itself by a rotation of 180o or
less
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Do You Get It?• Is this a reflection?
• How many lines of symmetry? Does it have rotational symmetry?
AA’
B
B’
CC’
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Do You Get It?• If point R (-4,-5) is reflected over the
y-axis, what are the coordinates of R’?
• If point S (0, 2) is reflected over the line x = -5, what are the coordinates of S’?
• Given points T ( -4, 3) and T’ ( -4, -2), what is the line of reflection?