Transformations a in mathematics is when a figure changes in some way. its and/ may change. transformations can be or when a transformation occurs, the original figure, or pre-image, is to generate the new transformed figure, ortriangle abc is mapped to triangle then a -> b -> and c -> note: the image will often use the same letters as the but with a in the top right corner. the letters with the tick marks are called the letter a' in the image is read “” translations ( under what happened to the triangle ) the triangle simply moved from to another. it did not or size. it did not therefore, a translation can be defined as the this is also known as a in geometry. a rigid motion is translations as functions the frog starts out at point (0, 0) on the coordinate grid. it then hops 3 spaces to the right and 2 spaces up. this can be represented by saying this can be treated like a function, also known as a by plugging in the original x- and y-coordinate values, or the input values, which will generate a new coordinate, or the output value. vectors a vector represents the difference of a ray and a vector is that a vector begins at the point and ends at the point. example 1 pg 5 hexagon waters is shown on the coordinate plane. hexagon waters is translated according to the rule: (x, y) → (x − 4, y − 7) graph hexagon w'a't'e'r's'. pre image rule (x-4, y-7) image w (3,5) a(5,5) t(6,3) e(5,1) r(3,1) s(2,3) example 2 pg 5 triangle cat is translated on the coordinate plane below to triangle c'a't'. if kite lion is translated according to the same rule that translated triangle cat, where is kite l'i'o'n' located? 1. find the rule from the trianlges ( x y 2. apply the rule to the kite pre image rule image l ( , ) i ( , ) o ( , ) n ( , ) reflections a is a transformation where the image of a figure is shown directly opposite, or across a notice that both figures are the and size. the segment lengths and angle measures have therefore, quadrilateral abcd is congruent to quadrilateral a'b'c'd'. reflections, along with translations, are types of line of reflection the is a unique line that is from the corresponding vertices of the pre-image and image. it is also to the line that connects these corresponding vertices. if a line is drawn connecting a and a', then that line will be to the and the intersection of the two lines will be the of a and a'. x-axis y-axis line y=x another way to say it (equation of the line) transformation rule (x, y)-> ( , ) (x, y)-> ( , ) (x, y)-> ( , ) example reflections across horizontal/vertical lines- notice that each point is the away from the as its corresponding point. for example, if point a is 4 units away from the line of reflection, point a' is from the line of reflection but on the reflections across diagonal lines you must first find the slope of the line of reflection. you will use this slope to find corresponding points. continue using the slope of the line of reflection to plot a point that is to the distance between point a and the line of reflection. this point is a', or example 1( page 9 ) pentagon house is shown on the coordinate plane. reflect pentagon house across the: x-axis (x, y)-> (x,-y) y-axis (x, y)-> (-x, y) y=x (x, y)-> (y, x) y=-2 x=1 h(-4,5) o(-2,3) u(-3,1) s(-5,1) e(-6,3) example 2 ( page 9) what two reflections took place to transform part to p”a”r”t” essential questions • how are translations and reflections represented as a function? • what is the relationship between translations, reflections, and rigid motion? • how do rigid motions affect a given figure?