Geometry: Translations, dilations, symmetry, rotations, and reflections.

Translation

When the position of an object is changed

Translations Rule

Changes the position of an object

A translation is always _______.

addition

The box next to a T of translation houses what?

The coordinates you translate by

Dilation

A figure is either enlarged or reduced by a scale factor of K

If K > 1, a dilation is an ________.

enlargement

If 0 < K < 1, a dilation is a _______.

reduction

Dilations rule

Enlarges or reduces the object

A dilation is always ________.

multiplication

D2 as a dilation means

Enlargement

D1/2 as a dilation means

reduction

The k in Dk in a dilation is

what to dilate by

Line symmetry

When an object can be folded onto itself

Rotational symmetry

When the object can be rotated onto itself after less that a full term.

To find the rotational symmetry, what’s the equation?

360/n

Point symmetry

When the object can be rotated onto itself after a half turn (180 degrees)

Rotation (turn)

A figure is moved about a fixed point called a rotation center

The box right next to an R means in a rotation

the degrees you rotate by

90 degrees is a ______ turn.

1/4

180 degrees is a ______ turn.

1/2

270 degrees is a _____ turn.

3/4

Letters that are different than the original have a small roman numeral in the ____ ______ corner of them.

top right

Rotation rules

Figure is turned about a fixed point

In a rotation about the origin, the original image turns ________ (___).

counterclockwise, (CCW)

90 degrees turn (270 degrees CW) ——- Rotation

(-y, x)

180 degrees turn (180 CW) ——- Rotation

(-x, -y)

270 degrees turn (90 degrees CW) ——- Rotation

(y, -x)

Origin ——- Rotation

(-x, -y)

Reflection (flip)

Mirror image of a figure or point

Glide reflection

Consists of a line reflection and translation (combination of 2 transformations)

The box next to an r in a glide reflection is

what to reflect over

Reflection rules

Mirror image of a figure or point

Over x-axis ———Reflection

(x, -y)

Over y-axis ———Reflection

(-x, y)

Over y = x ———Reflection

(y, x)

Over origin ———Reflection

(-x, -y)

Over y = -x ———Reflection

(-y, -x)

Reflecting over a point

The point you are reflecting over becomes the midpoint

What equation do you use to reflect over a point?

The midpoint formula

What number is to the right side of the = in the midpoint formula when solving?

The rbox numbers