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Geometry - Transformations

Terms in this set (24)

Transformations
an operation that maps an original geometrical figure, the pre-image onto a new figure called the image

a transformation can change the position, size or shape of the figure

Types of transformations:
line reflections
point reflections
rotations
translations
dilations
Pre-image
The original figure in a transformation.
Image
figure
Reflection
A transformation that "flips" a figure over a mirror or reflection line.
Translation
A transformation that "slides" each point of a figure the same distance in the same direction.
Rotation
A transformation that turns a figure about a fixed point at a given angle and a given direction.
Isometry
A transformation that preserves size and shape. The image of a figure under an isometry is congruent to the original figure. Also called a rigid transformation.
Rigid Motion
transformations that preserve distance and angle measurements a
line reflection
a transformation that uses a line of reflection to create a mirror image of the original figure
dilation
A transformation that changes the size of an object, but not the shape.
point reflection
for every point in a figure, there is another point found directly opposite on the other side of the center such that the point of a reflection becomes the midpoint. Figures do not change size.
symmetry
occurs when two halves of a figure mirror each other across a line
line of symmetry
is the line that divides the figure into 2 mirror images
line of reflection
The line over which a figure is reflected. The vertices of the original and new figure are the same distance from this.
horizontal symmetry
when cut horzantally in half both sides are the same
vertical symmetry
when cut vertically in half, both sides are same
preserving distance
keeping the distance between the 2 points the same
(examples; translation,reflection,rotation)
preserving angle measurement
keeping the angles measure the same
(examples: translation, reflection, rotation and dilation)
point symmetry
an object has point symmetry if it is the same figure after a rotation of 180 degrees

(letter H, king of hearts)
rotational symmetry
image is the same after a rotation of a certain number of degrees
(square)
composition of Transformation
is a combination of 2 or more transformations

in a composition you perform each transformation on the image of the preceding transformation
glide reflection
is the composition of a line reflection and a translation whose direction is parallel to a line of reflection

(footprints)
vector
a directed line segment which is a segment with an arrow at one end indicating the direction of movement.

a vector has a specific length
isometrics
transformations that preserve distance
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