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Transformation

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

Preimage

the original figure

Image

a figure resulting from a transformation

Isometry

a transformation in which the preimage and image are congruent

Translation

A transformation that "slides" each point of a figure the same distance in the same direction.

(x+/-a, y+/-b)

Writing Rules for Translations

Reflection

A transformation that "flips" a figure over a mirror or reflection line.

Line of Reflection

A line that a figure is flipped across to create a mirror image of the original figure

*perpendicular to lines connecting corresponding points of the image and preimage

*perpendicular to lines connecting corresponding points of the image and preimage

(x, -y)

Rule for Reflection Over X-axis

(-x, y)

Rule for Reflection over Y-axis

(y, x)

Rule for Reflection Over line y=x

Rotation

a transformation in which a figure is turned around a point

-counterclockwise unless stated otherwise

-counterclockwise unless stated otherwise

(-y, x)

Rule for 90 degree rotation

(-x, -y)

rule for 180 degree rotation

(y, -x)

rule for 270 degree rotation

Dilation

A transformation that changes the size of an object, but not the shape.

-image will always be similar to preimage

-image will always be similar to preimage

(nx, ny)

Rule for Dilations

n^2 x area of preimage

Area of Image of Dilation

add numbers in corresponding positions

-matrices must be same size

(translation)

-matrices must be same size

(translation)

Adding Matrices

multiply the number by every number in matrix

(dilation)

(dilation)

Multiplying Matrices by a Single Number

Vertex Matrix

a matrix used to represent the coordinates of the vertices of a polygon

[1 0]

[0 -1]

[0 -1]

Matrix for Reflection over X-axis

[-1 0]

[0 1]

[0 1]

Matrix for Reflection over Y-axis

[0 1]

[1 0]

[1 0]

Matrix for Reflection over Y=X

[0 -1]

[1 0]

[1 0]

Matrix for 90 degree Rotation

[-1 0]

[0 -1]

[0 -1]

Matrix for 180 degree Rotation

[0 1]

[-1 0]

[-1 0]

Matrix for 270 degree Rotation

[1 0]

[0 1]

[0 1]

Matrix for 360 degree Rotation

the shape is rotated 180 degrees

what happens when you have a scale factor that is negative?

connect the corresponding points of the image and preimage and construct the perpendicular bisector

How do you construct the line of reflection?