30 terms

# Hn. Math 2- Transformations Quiz #1

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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
(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
(-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
(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)
Adding Matrices
multiply the number by every number in matrix
(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]
Matrix for Reflection over X-axis
[-1 0]
[0 1]
Matrix for Reflection over Y-axis
[0 1]
[1 0]
Matrix for Reflection over Y=X
[0 -1]
[1 0]
Matrix for 90 degree Rotation
[-1 0]
[0 -1]
Matrix for 180 degree Rotation
[0 1]
[-1 0]
Matrix for 270 degree Rotation
[1 0]
[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?