vocabulary: transformation – a one-to-one correspondence between two sets of points pre-image...
Post on 17-Dec-2015
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Lesson 1
Vocabulary:
Transformation – a one-to-one correspondence between two sets of points
Pre-image – the original figure
Image – figure after transformation
Vocabulary cont’d
Center of dilation – the point which is used as a reference point for a dilation
Line of reflection – the mirror; the line over which an image is reflected
Isometry – a transformation that preserves distance and angle measure
Translation – a slide; a transformation where all the points in the image are the same distance from their corresponding points in the pre-image
Reflection – a transformation where all points on the image are the same distance from the line of reflection as their corresponding points in the pre-image
Dilation – a transformation where a figure is increased or decreased in size by a factor (the points of the image are at the distance of their corresponding points, on the pre-image, from the center of dilation multiplied by the factor)
Lesson 2
A reflection through line l of point P creates P’. Line l is then the perpendicular bisector of segment PP’.
Defining other transformations through reflections
Translation – the composite of two successive reflections through parallel lines
Rotation – the composite of two successive reflections through intersecting lines› Center of rotation – the point about which a
rotation occurs› Magnitude – the measure of the angle through
which a point of the original figure turns to coincide with its rotation image
Lesson 3
Vocabulary: Congruent – two figures are such if there exists an
isometry such that one figure is the image of the other
Glide Reflection – the composite of a translation and a reflection over a line parallel to the direction of the translation (in a sense, three or some greater odd number of reflections)
Mirror Image – created by an odd number of reflections, two figures are the reverse of one another
Lesson 4
Vocabulary: Rotation symmetry – a figure possesses this
characteristic, with respect to a point, iff it coincides exactly with its rotation image when rotated less than 360˚ about the specific point (the center of the figure is usually said point)› A figure has point symmetry if it looks exactly the same
turned upside down
n-fold rotation symmetry – a figure has this iff the smallest angle through which it can be turned to look exactly the same is 360˚/n› A figure with point symmetry has 2-fold symmetry
Vocabulary cont’d
Reflection (line) symmetry – a figure has this, with respect to a line, iff it coincides with its reflection image through the line› The line is sometimes called the axis
Translation symmetry – a patter has such iff it coincides with a translation image
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