Unit 1.3 Tranformations test STUDY GUIDE

What is a transformation?

maps or moves an pre image onto a final image. Images are labeled with prime marks.

What is a reflection?

Folding or flipping an object over the line of reflection.

reflection in y-axis

(-x,y)

reflection in x-axis

(x,-y)

reflection y=x

(y,x) diagnol line with a positive slope

reflection y=-x

(-y,-x)

What is isometry?

A rigid transformation that maps every figure onto a congruent figure so that the image and the pre-image are congruent figures.

Translation Function

(X +_#, Y+_#)

Vector Notation

< +_ #, +_#>

Translation Function VS Vector Notation

changes () to <>, and changes x & y to numbers.

90 CCW and 270 CW

(-y,x)

180 CCW and 180 CW

(-x,-y)

270 CCW and 90 CW

(y,-x)

360 CCW and 360 CW

(x,y)

A negative angle of rotation

turns the figure clockwise (positive)

A positive angle of rotation

turns the figure counterclockwise (negative)

What is a glide reflection?

a mirror reflection followed by a translation parallel to the mirror. (slides)

Composite of Transformations

your new prime image becomes your pre image for the 2nd transformation. 2 PRIME MARKS.

Reflection in parallel lines theorem

A composition of TWO reflections in parallel lines that results in a translation

What happens in reflection in parallel lines theorem?

the distance between the AA" is doubled.

Reflections in intersecting lines theorem

two reflections over two lines that intersect, the result is equivalent to a single rotation transformation of the original object.

What happens in reflections in intersecting lines theorem?

the angle of rotation is 2x where x is the measure of the acute or right angle formed by lines k and m.

Congruent

same shape and size

What is it called when the figures aren't congruent

they are similar but non congruent

What is perpendicular in the reflections in parallel lines theorem?

The pre-image to the image

if they give you the rotation of the angle, what do you do?

you divide the rotation number by 2.