Definitions
the original figure before a transformation
preimage
a transformation in which a figure is turned about a fixed point
rotation
a transformation where a figure is flipped over a light. also called a flip
reflection
a transformation that slides a figure from one position to another without turning
translation
If the size of my figure changes is it a rigid motion?
NO
the resulting figure after a transformation
image
a fixed point around which shapes move in a circular motion to a new position
center of rotation
the line over which is reflected
line of reflection
If a figure is translated left 4 and up 3 units. What is the translation rule?
(x,y) -> (x-4, y+3)
does a square have rotational symmetry?
if yes, what is the least amount of degrees I can rotate it for it to land back on itself?
yes
90 degrees
an operation that maps a geometric figure, preimage, onto a new figure, image.
transformation
the degree measure of the angle through which a figure is rotated
angle of rotation
what steps do you take to reflect a shape over the x axis?
Count how many points away from the x-axis it is, then count that many units in the OPPOSITE direction. Repeat for all points.
If a figure is translated left 1 and down 3 units THEN rotated 270 degrees. starting at (x,y), give the translation rule, THEN the rotation rule from the new point.
(x,y) -> ( , ) -> ( , )
(x,y) -> (x-1,y-3) -> (y-3,-x+1)
the preimage is point (5,-1) and the image is point (9,4) what is my translation rule?
(x+4,y+5)
having the same measure; if one image can be obtained by another by a sequence of rotations, reflections, or translation
congruent
if we were to rotate a triangle 90 degrees clockwise, what direction would that be?
right
sketch what it would look like to reflect a triangle over the x-axis (stripes), THEN reflect over the y-axis.(filled in)
see ms.lee's work
the preimage is point (-3,6) and the image is point (4,5) what is my translation rule?
(x+7,y-1)
What type of transformation slides a figure without changing its size or shape?
Translation
an operation that maps a geometric figure, preimage, onto a new figure, image.
transformation
What are the rotation rules for 90, 180, and 270 degrees
90: (x,y) -> (-y,x)
180: (x,y) -> (-x,-y)
270: (x,y) -> (y,-x)
A point P(–2,5)P(–2, 5)P(–2,5) is reflected across the x-axis, and then its image is reflected across the y-axis. What are the final coordinates?
(2,–5)
If a figure is translated right 5 and up 2 units THEN rotated 90 degrees. starting at (x,y), give the translation rule, THEN the roation rule from the new point.
(x,y) -> (x+5, y+2) -> (-y-2, x+5)
A point (−4, 5) is reflected across the y-axis, then translated 3 units down. What are the final coordinates?
(4, 2)