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Transformation

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

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Preimage

the original figure

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Image

a figure resulting from a transformation

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Isometry

a transformation in which the preimage and image are congruent

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Translation

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

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

Writing Rules for Translations

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Reflection

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

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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

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(x, -y)

Rule for Reflection Over X-axis

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(-x, y)

Rule for Reflection over Y-axis

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(y, x)

Rule for Reflection Over line y=x

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Rotation

a transformation in which a figure is turned around a point

-counterclockwise unless stated otherwise

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(-y, x)

Rule for 90 degree rotation

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(-x, -y)

rule for 180 degree rotation

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(y, -x)

rule for 270 degree rotation

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Dilation

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

-image will always be similar to preimage

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(nx, ny)

Rule for Dilations

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n^2 x area of preimage

Area of Image of Dilation

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add numbers in corresponding positions

-matrices must be same size

(translation)

Adding Matrices

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multiply the number by every number in matrix

(dilation)

Multiplying Matrices by a Single Number

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Vertex Matrix

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

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[1 0]

[0 -1]

Matrix for Reflection over X-axis

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[-1 0]

[0 1]

Matrix for Reflection over Y-axis

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[0 1]

[1 0]

Matrix for Reflection over Y=X

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[0 -1]

[1 0]

Matrix for 90 degree Rotation

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[-1 0]

[0 -1]

Matrix for 180 degree Rotation

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[0 1]

[-1 0]

Matrix for 270 degree Rotation

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[1 0]

[0 1]

Matrix for 360 degree Rotation

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the shape is rotated 180 degrees

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

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

How do you construct the line of reflection?

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