Transformations Flashcards
What does it mean to preserve distance?
Lengths of segments are the same
What does it mean to preserve angle measure?
Angles stay the same
What does it mean to maintain parallelism?
Things that were parallel are still parallel
What does it mean to maintain collinearity?
Points on a line stay on the line
What is a rigid motion?
A transformation preserving distance, angle measure, parallelism, & collinearity
What does a rigid mroion to ensure?
Resulting figure is same size & shape (congruent image & pre image)
Which transformation is NOT a rigid motion?
Dialation- not same size
What is a stretch?
One dimension’s scale factor is different than the other dimension’s scale factor
What is a dialation?
The scale factor is the same for both dimensions, producing a PORPORTIONAL but not IDENTICAL shape
What are the properties of a translation (slide)
- Distances are the same- AA’ is congruent to BB’
- Orientation (way something is angled) is the same
- Each translated segment is parallel to its image ex. AC is parallel to A’C’
Translation mapping
(x,y) —> (x-7, y-3)
Translation description
7 units left and 3 units down
Translation notation
T(x,y), T(-7,-3)
Translation vector
___
V = (-7,-3)
How to find vector that defines translation &magnitude
- Count spaces between both images
Ex. 3to the second power + 2to the second power= V*to the second power
Square root for answer
What do you write when finding the rule describing the given translation?
T(x,y)
What is a reflection?
A rigid motion where each point of the pre image has an image that is the same distance from the LoR as the original point (on the opposite side of the line)
What is the line of reflection?
The perpendicular bisector of the segment
Reflection properties #1- if point P is not on line m, what is line m?
The perpendicular bisector of PP’
Reflection properties #2- what is point p if it is on line m?
Congruent to P’ P=P’
What is reversed about the figure in a reflection?
Orientation
Line reflection rule #1- reflected over x axis
(x,y) to (x,-y)
Line reflection rules #2- reflected over the y axis
(x,y) to (-x,y)
Line reflection rules #3- when y=x and y=-x
FLIP- (x,y) to (y,x) / (x,y) to (-y,-x)
What is function notation
R (P) = P’
m
What is line of symmetry/reflectional symmetry?
A line can be drawn through the figure so both sides of the figure are mirror images of the other (there can be more than one LoS or no LoS)
What is point symmetry?
The figure is the same image when rotated 180 degrees, or turned upside down (looks the same!)
What us always true about reflections?
The segments of both the image and pre image are congruent to each other
Point F is on one side of line g and is exactly 4 cm away from line g. Point H is on the opposite side of line g and is also exactly 4cm away from line g- is it safe to say Point H is the reflection of Point F?
No- there is no proof line g is the perpendicular bisector
What changes in the properties of rotations?
The distances are different- points on the plane move different distances, depending on distance from center of rotation. The image and pre-image segments are not parallel to each other because of incongruous distances
What stays the same in rotation properties?
Orientation & Special points- center of rotation is invariant (constant)
Rotation of 90 degrees
(x,y) to (-y,x)
Rotation of 180 degrees
(x,y) to (-x,-y) flip!!
Rotation of 270 degrees
(x,y) to (y,-x)
After a figure is rotated, A = A’. What does this mean?
The center of rotation is A (why?)
How do rotations differ from reflections & translations?
Not translation- each point moves different distances
Not reflection- same orientation
Why isn’t dilation a rigid motion?
It does not preserve distance
What does every dialation have?
A center (generally origin( and scale factor n
What is the dialation called if the scale factor n>1?
Enlargement
What is the dilation called if 0
Reduction
What happens if the scale factor in a dialation is 1?
Nothing
Dialation notation
D (x, y) = (kx, ky)
O,k O= center of dialation, k= scale factor
Which properties ARE preserved in dilations?
Angle measures (angles are the same), Parallelism (dilations create parallel lines between all pre image and image corresponding segments), and Collinearity (points on the line remain on that line)
