Geometry: Transformations
to rotate a point about the origin (point 0, 0) 180° clockwise (CW)
(x, y) becomes (-x, -y)
to reflect a point around the origin
(x, y) becomes (-x, -y,)
to reflect a point over the y-axis
(x, y) becomes (-x, y)
to reflect a point over the line y = -x
(x, y) becomes (-y, -x)
to rotate a point about the origin (point 0, 0) 270° clockwise (CW)
(x, y) becomes (-y, x)
from the origin, to dilate by a factor of "c" ...
(x, y) becomes (cx, cy)
to translate a figure 6 units to the right and 4 units down ...
(x, y) becomes (x + 6, y - 4)
to translate a point 6 units to the right ...
(x, y) becomes (x + 6, y)
to reflect a point over the x-axis
(x, y) becomes (x, -y)
to rotate a point about the origin (point 0, 0) 360° clockwise (CW)
(x, y) becomes (x, y)
to rotate a point about the origin (point 0, 0) 90° clockwise (CW)
(x, y) becomes (y, -x)
to reflect a point over the line y = x
(x, y) becomes (y, x)
to rotate 180° clockwise is the same as...
180° counter clockwise
to rotate 90° clockwise is the same as...
270° counter clockwise
to rotate 360° clockwise is the same as...
360° counter clockwise AND will look like the original position
to rotate 270° clockwise is the same as...
90° counter clockwise
isometry
a distance preserving length and angles
pre-image
a figure before a transformation has taken place
reflection line
a line that is the perpendicular bisector of the segment with endpoints at a pre-image point and the image of that point after a reflection
reflection
a transformation that "flips" a figure over a line of reflection
translation
a transformation that "slides" each point of a figure the same distance in the same direction
dilation
a transformation that changes the size of an object, but not the shape
rotation
a transformation that turns a figure about a fixed point through a given angle and a given direction
transformation
an operation that moves or changes a geometric figure in some way to produce a new figures
to reflect a figure over the line y = 2
each point of the pre-image and the image will be the same distance away from the horizontal line of reflection
to reflect a figure over the line x = 2
each point of the pre-image and the image will be the same distance away from the vertical line of reflection
The dilation of a shape _______________ or _________________ that shape .
enlarges ... reduces
∆ABC transforming to ∆A'B'C' indicates an ____________________ of the figure ∆ABC to a new location ∆A'B'C', and as a result, ∆ABC and ∆A'B'C' remain congruent.
isometry ... congruent
Isometry is a ______________ of a geometric figure to another ______________________ using a reflection, rotation or translation.
map ... location
Transformation is the ________________, or _________________, of all points of a figure in a plane according to a common operation.
mapping, or movement,
A reflection provides a ___________ _____________ over a given line.
mirror image
A rotation ____________ a shape around a given ________________.
moves ... point
The _________________ of the coordinate plane is point (0, 0).
origin
An example of using a _____________ is when a pre-image is transformed from ________________.
prime ... A ---> A'
A translation ______________ all of the points of a shape according to given _____________________.
slides ... directions
angle of rotation
the amount of rotation (in degrees) of a figure about a fixed point such as the origin
scale factor
the ratio used to enlarge or reduce similar figures
image
the result of a transformation of a point, line, or figure
prime
the small hash mark that you put next to the point labels of the image, for example: A ---> A'
Types of transformations include _________________, ___________________, and ____________________.
translation, reflection, and rotation
The direction of a translation may be ________ or _________ or ____________ to _________________.
up or down ... right to left
