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.

None – Go Hawks!!!

Back

One – Go Bulls!!!

Back

Almost one… Go Bears!!!

Back

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?