Transformations
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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)