Ch. 4 1st Quiz Flashcards
Translation
Movement without change of attributes to the figure.
Component Form
Combination of horizontal/vertical components. Written like an ordered pair.
Coordinate Form
Describes a single point in a coordinate plane.
(x,y)
X- how far left or right the point is
Y- how far up or down the point is
Reflection
A transformation over line m that maps each pt
Known as a flip. A reflection is a mirror image of the shape. The image will reflect through the reflection line.
X-axis Reflection
(x,y) -> (x,-y)
Y-axis Reflection
(x,y) -> (-x,y)
y = x
(x, y) -> (y,x)
When y=# or x=#…
Count from line to another side
Glide Reflection
Composition of Translation/Reflection
How to show the minimum distance
1] Reflect one pt. over x-axis
2] Find eq. of new line
3] Plug in zero for y
Rotation
Transformation in which a figure is turned about a fixed point called the center of rotation.
Clock-Wise Rotation 90 degrees
(x,y) -> (y,-x)
Counter Clock-Wise Rotation 90 degrees
(x,y) -> (-y,x)
Clock-Wise and Counter Clock Wise Rotation 180 degrees
(x,y) -> (-x,-y)
Clock-Wise Rotation 270 degrees
(x,y) -> (-y,x)
Counter Clock-Wise Rotation 270 degrees
(x,y) -> (y,-x)
Congruent Figures
Two figures are congruent iff there is a rigid motion or a composition of rigid motion.
Rigid Motion/Isometry
When you move it, its attributes don’t change
Double Reflection - Translation
Better Definition
If two lines are parallel, then two reflections equal a translation
Double Reflection - Rotation
If two lines intersect at a pt, then a reflection in the vertical line followed by a reflection in the horizontal line is a rotation about the point.
Angle of Rotation
The angle of rotation about a point is 2 times the original acute or right angle.
Dilation
Transformation in which a figure is enlarged or reduced w/ respect to a fixed point.
True or false:
Dilation is an isometry
False
Dilation is not an isometry
True or false:
Dilation is an isometry
False
Dilation is not an isometry
Scale Factor
The ratio of lengths corr. sides of image and pre-image.
Formula for scale factor of dilation
K= CP1/CP
Enlargement vs. Reduction
K>1 (enlargement)
K<1 (reduction)
Notes to remember
If P is the center point (C), then P=P1
If P is not the center point (C), then P1 lies on ray CP
Angles are preserved
Coordinate rule for dilation
If P(x,y) is a pre-image of a pt, then its image after dilation is centered at the origin (0,0) w/ scale factor K is pt. P1 (kx, ky)
LOS Equilateral Triangle
3
LOS Regular Pentagon
5
LOS Rhombus
2
LOS Kite
1
LOS Isotrap
1
LOS Square
4
LOS Hexagon
6
LOS Rectangle
2
LOS Parallelogram
0
