Module 2 Transformations

Transformation

Is a change in the position, shape, or size of a figure.

Rotational Symmetry

Is a rotation that maps a figure back on to itself.

Lines of symmetry

Is equidistant from all corresponding pairs of points.

Glide reflection

A composition of translation and a reflection.

Rotation

A rigid motion that turns a figure about a fixed point called the center of rotation.

Identify Transformation

A rotation of 360 degrees will always map a figure on to itself.

Rigid Motion

A transformation that changes only the position of the figure (length and angle measures are preserved). Examples include rotations, reflections and translations.

Correspondence

Between two triangles is a pairing of each vertex of one triangle with one and only one vertex of another triangle. This pairing can be expanded to figures other than triangles and could also involve sides.

Construct Reflection

Create circle between Point __ and any point on the L.O.R. place pointy bit of compass on the chosen point of the L.O.R., and place the pencil bit on Point __. Draw a circle. Reverse the positions of the bits of the compass and create another circle. Where the circles intersect is your reflected Point __.

Point Symmetry

Created by the image and the pre-image when reflecting an object through a point.

Construct a Center of Rotation

Draw line from Point __ to Point __'. Bisect line. Repeat for another set of points. The intersection of the bisectors is your C.O.R

Angle of rotation

Is the number of degrees the figure rotates. A positive angle of rotation turns the figure counterclockwise (a negative angle of rotation can be used for clockwise rotation).

Image

Is the result of a transformation of a figure (called the pre-image). The image of point A is A' (read as A prime).

Direct isometry

Isometry that preserves size and the order(orientation) of the vertices. These include translation and rotation.

Opposite isometry

Isometry that preserves the size, but the order of the vertices changes. This includes reflection.

Translate a Figure

Mark a point P that will become one vertex of the triangle. Set the compass width to the length of Segment AC (example). From P, draw an arc. Mark a point R on this arc. Set the compass width to the distance AB (example). From P, draw an arc roughly where the third vertex will be. Set the compass width to the distance BC (example). From R, draw an arc across the first, creating point Q. Connect points.

Construct Line of Reflection

Place pointy bit of compass on Point __, and pencil bit on Point __'. Draw a circle, and bisect it.

How do you find the degree of rotational symmetry for a regular polygon?

Take the # of sides and divide by 360.

Congruent

There is a rigid motion (or a composition of rigid motions) that maps the pre-image onto the image.

How are vectors used to define translations?

They give you the distance and direction to translate the figure.

Composition

When a series of rigid motions takes place with one rigid motion building off another.

Isometry

is a transformation that does not change in size. These include all of the rigid motions: reflections, translations and rotations.

Which rigid motions depend on perpendicular bisectors?

reflection and rotation