Transformations Flashcards
Transformation
The set of all points of a figure(preimage) is mapped to a different set of all points(image) if and only if the mapping is a transformation
Image
The set of all points that are the result of the transformation
Preimage
The set of all points that are being mapped
One-to-one mapping
When every element of the first set is mapped to each and exactly one element of the second set.
Isometry
Also known as congruence mapping, If the mapping transforms lines to lines, preserves the length, and preserves angle measures then it has isometry.
rigid motion
A motion that has isometry is said to be a rigid motion
translation
A transformation that moves the image in one direction along a plane. Sometimes it is referred to as a glide transformation
reflection
A transformation that looks like a flipped image over a line. The set of all points is moved along a perpendicular guideline across the line of reflection to the opposite side such that the image is the same distance on the opposite side of the preimage.
line of reflection
The line used for reflecting; the preimage is equidistant to the line when compared to the image.
Rotation
The transformation maps each point around the point of rotation by the angle of rotation. It looks like a spin movement around the pivot of the given point.
Point of rotation
The point used as the vertex for the degree of angle created to rotate a preimage to its image or “pivot around” for rotations
Angle of rotation
The degree or radian measure given that is used to rotate
Clockwise/counterclockwise
The directions on the clock. You can use it in 4 different quadrants. It will go in either direction depending on which one it is.
Dilation
A transformation that moves the shape and changes its size by its scale factor. Dilations are not isometric.
Point of dilation
The point of dilation is the point used to create the dilation lines from the shape.
Scale factor
the factor that is multiplied by the distance between the preimage and point of dilation then used its result to find the image position
enlargement
Occurs when the absolute value of the scale factor is greater than 1 it causes the image to be larger than the preimage.
Reduction
Occurs when the absolute value of the scale factor is between 0 and 1 causing the image to be smaller than the preimage
Composite transformation
Is a transformation that is completed by doing multiple transformations together. Sometimes a composite transformation can be equivalent to a different one-step transformation.
Glide reflection
Composite transformation comprises of a translation with a reflection such that the translation occurs along the same direction as the line of reflection.
Vector
A vector is an object that has both a magnitude and a direction. Geometrically, we can picture a vector as a directed line segment, whose length is the magnitude of the vector and with an arrow indicating the direction.
Linear symmetry
When an object is cut exactly in the middle, to form two identical parts, then the first is said to be symmetrical to the other. Likewise when we draw a line segment exactly in the middle of a pattern or drawing, if one part is identical to the other then the pattern is said to be linearly symmetrical.
Line of symmetry
A line of symmetry is a line that cuts a shape exactly in half. This means that if you were to fold the shape along the line, both halves would match exactly. Equally, if you were to place a mirror along the line, the shape would remain unchanged.
Rotational symmetry
A shape has rotational symmetry if it looks the same after being rotated (by less than 360°). The center of rotation is the point around which a shape is being rotated.
Translations
A translation moves a shape without any rotation or reflection. For example, the square on the left has been translated 2 units up (that is, in the positive y-direction) to get the square on the right. Rotating an object means turning it around a point, which is called the center of rotation.
Reflections
Reflections are a type of transformation where a figure is flipped to the opposite side of a line of symmetry. A line of symmetry can lie anywhere in the coordinate plane. In particular, Polygons and functions can be reflected over the x-axis, the y-axis, the origin, and the line y = x.
Rotations
A rotation is a transformation that turns a figure about a fixed point called the center of rotation. An object and its rotation are the same shape and size, but the figures may be turned in different directions. Rotations may be clockwise or counterclockwise.
