Transformations Flashcards
Line symmetry
Congruent if folded horizontally vertically or diagonally along an imaginary line
Point symmetry
If identical when rotated 180 degrees upside down
r x-axis
Reflect over x axis, negate y
r y-axis
Reflect over y axis negate x
r y=x
Diagonal up, flip (y,x)
r y=-x
Diagonal down, flip/negate both (-y,-x)
What is not preserved in a line reflection?
Orientation
R 360
Original (a,b)
R 90
(-b,a)
R 180
(-a,-b) same as point reflection through origin
R 270
(b,-a)
R -270
(-b,a)
R -180
(-a,-b)
R -90
(b,-a) negatives go clockwise
What is preserved under rotation?
Distance, orientation, midpoint, collinearity, angle measure
Rotational symmetry
Figure is the same under a rotation, for regular shapes divide 360/#sides for the order of rotational symmetry
R o
Point reflection through the origin, (-x,-y)
How do you reflect though points other than the origin?
Find the rise and run from the point to the point you are reflecting over and continue the line with that slope so the point you are reflecting over is the midpoint
What is a glide reflection?
Composition of a translation and a line reflection, orientation is not preserved
A composition of 2…
Translations is a translationRotations is a rotation
(Don’t have to memorize but good to know) A composition of 2 line reflections through…
Parallel lines is a translation Perpendicular lines is a point reflectionIntersecting lines is a rotation
What is Isometry/rigid motion, and an example of not isometric?
Transformations that preserve distance, dilations are the only ones not isometric
Direct Isometry
Preserves orientation:TranslationsRotationsPoint reflections
Opposite Isometry
Does not preserve orientation:Line reflectionsGlide reflections
How do you know if it preserves orientation?
Write out the order of point going clockwise for both figures and see if it’s in the same order e.g. ABCABCABC vs BCABCABCA has preserved orientation