transformations Flashcards
what is a reflection?
takes each point to another point that is equidistant from a given line on the other side
line segment that connects original point and image is perpendicularly bisected by the line of reflection
what is a translation?
moves each point to another point by a directed line segment (vector)
segment that connects original point and image is parallel to the given segment and the same length and direction
what is a rotation?
takes points and rotates them around a given center by a given amount of degrees in a certain direction
the original point and the image will be equidistant from the center of rotation
the angle created by the point, its image, and the center of rotation will be equal to the given rotation
what is a rigid transformation?
a transformation that maintains congruency
doesnt change size or shape
translation, rotation, and reflection
what is the parallel postulate?
given a specific line and a point not on the line, there is only one parallel line that passes through that point
what makes a figure congruent?
have the same size and shape
can take one figure to the other with only rigid transformations
how do you do reflection with constructions?
create an arc centered at the given point that crosses through the line of reflection twice
draw a perpendicular bisector to the line segment that connects the intersections between the arc and the line of reflection
draw a circle centered at the intersection between the perpendicular bisector and the line of reflection with a radius that goes to the original point
the image will be the intersection between this final circle and the perpendicular line
what is reflectional symmetry?
when a line that passes through a figure can take the figure onto itself
splits it up into two exactly congruent halves
what is rotational symmetry?
when a rotation around the center of the figure can take the figure onto itself
if you rotate the figure in place and it looks the same
