12.1 – reflections 12.5 – symmetry m217 – geometry
TRANSCRIPT
12.1 – Reflections12.5 – Symmetry
M217 – Geometry
ISOMETRY
A movement or “translation” of a figure that preserves its original dimensions. Reflections Translations Rotations
CC
Reflection – A transformation that uses a line that acts like a
mirror. Reflection
Line of Reflection
Reflection Properties: Over y-axis(x, y) → ( )A (-2, 4)
B (2, -1)
C (0, 4)
D (-3, 0)
Reflection Properties: Over x-axis(x, y) → ( )A (-2, 4)
B (2, -1)
C (0, 4)
D (-3, 0)
Reflection Properties: Over y=x(x, y) → ( )A (3, 4)
B (1, 1)
C (-3, 2)
D (-32, 11)
y = x
Ex: Reflection in the line y=1
y = 1
A (-1, 3)
B (3, -2)
C (0, 1)
D (-2, 0)
Ex: Reflection in the line x = -2
x = -2
Triangle ABC: A (-1, 3) B (-3, -2) C (-4, 1)
The Line of Symmetry is the imaginary line where you could fold an image and have both halves match
exactly.
The Line of Symmetry is the imaginary line where you could fold an image and have both halves match
exactly.
Determine the number of lines of symmetry in each logo
1.
2.
3.
4.
5.
How many does the Mercedes logo have?
How many does the Star of David have?
Rotational Symmetry : if a figure can be mapped onto itself by a rotation of 180o or
less
rotational symmetry : if a figure can be mapped onto itself by a rotation of 180o or
less
rotational symmetry : if a figure can be mapped onto itself by a rotation of 180o or
less
rotational symmetry : if a figure can be mapped onto itself by a rotation of 180o or
less
Do You Get It?• Is this a reflection?
• How many lines of symmetry? Does it have rotational symmetry?
AA’
B
B’
CC’
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?