Henry County Schools

 TRANSFORMATIONS TRANSFORMATION: A general way to describe a ____________________ done to a ___________________, ____________________, or ______________________. The _____________ shape is called the “____________________”, the __________________ is called the “______________________”Every point in the pre-image is accounted for in the image. Notation: A→A'Translations:Reflections:Rotations:Dilations:TRANSLATIONSDefinition: The process of _________________ an object from one place to another. Notation: T(a,b) The value of ____ tells us how to move in the _______ direction. The value of ____ tells us how to move in the _______ direction. Example 1: Find the image of Point A under the translation T(3,-2) Example 2: Write a rule to describe the translation of C-> C’Example 3: The chart below shows the coordinates for the vertices of Triangle ABC Triangle ABC undergoes a translation of T(5,1) resulting in Triangle A’B’C’. What are the coordinates of the vertices for the new triangle? Which quadrant would the new triangle be in?____________________REFLECTION OVER THE Y-AXIS Draw the reflection across the y axisLooking at the graph above, is there a pattern between the pre-image and image?Point M ( ____ , _____) → M’ (_____ , _____) To reflect a point in the y- axis multiply its ____ coordinate by ____. Or change it to the ___________. The ___ coordinate stays the ___________.The rule for y-axis reflection is (x,y) → (_____ , ____) Examples: State the prime coordinates after a reflection over the y –axis.(1, 3) → 2) (-3,4)→ 3) (-8, 11) 4) (0, 5) REFLECTIONS OVER THE X AXIS Label your x and y axis. Let’s check: Original figure -> image -19049995250Point A (____, _____) -> A’(_____, ______) To reflect a point in the x-axis, multiply its _____ coordinate by ______. Or make it the ____________. The _____ coordinate stays the ______. The rule for x-axis reflection (x,y) → (_____, ______) Examples:Example 1: State the prime coordinates after a reflection over the x axis. (1,3)→ ( , ) (-3, 4) → ( , ) (0,4) → ( , ) (-2, -2)→ ( , )Example 2: Sketch the reflection of triangle FGH across the x-axis on the grid below. Give the coordinates of the pre-image and image. -19049937147527336759525F ( , ) F’ ( , ) H ( , ) H’ ( , ) G ( , ) G’ ( , )27336759525REFLECTIONS OVER CERTAIN LINES Draw the line y = 2 on the graph belowDraw the line x = 2 on the graph below366712527114509525Now graph the point A (-3, 4) on each coordinate plane. Each point of a reflected image is the ________ distance from the ____________ (the lines your originally drew) as the corresponding point of the __________ image. The _________________________ lies directly in the __________________ between the figure and its image. Reflect the point A over the given lines in each example above. More Examples REFLECTIONS OVER Y = X -1904992305050Reflection over the line y = x. On the graph to the left, graph the line y =x. Lets check: Original figure__> Image. Point A (2,4) → A’ (____, _____). To reflect a point in over the line y = x, you must switch the values for the ___ coordinate and the _____ coordinate. The rule for a reflection in the line y = x is (x,y)-->(______, _____) Example 1 : State the coordinates of the image after .1. A(4,5)→ A’( , ) 2. D(-1, 8) → D’( , ) 3. K(0,2) → K’( , ) 4. M(-3, -9)→ M’( , )Example 2: Triangle SUN has coordinates S(0,6), U(3,5), and N(1,3). On the grid, draw and label . Then, graph and state the coordinates of , the image of after a reflection in the y = x.REFLECTIONS OVER Y = -X29622750Reflection over the line y = -xOn the graph to the write, graph the line y = -x.Let’s check: Original Figure - Image Point A ( 2 , 4 ) ( , )To reflect a point in over the line y = -x, you must switch the values for the _______ coordinate and the __________ coordinate. As well as multiply each coordinate by negative 1. The rule a reflection in the line y = -x is: (x,y) (______, ______).29622750Example 1: State the coordinates of the image after reflection over y = -x1. A(4,5)→ A’( , ) 2. D(-1, 8) → D’( , ) 3. K(0,2) → K’( , ) 4. M(-3, -9)→ M’( , )Example 2: Triangle ABC has coordinates , , and . On the accompanying set of axes, graph, label, and state the coordinates of , the reflection of in the line y = - x.ROTATIONS34861509525-3809990In the figure to the right, the quadrants are labeled on the coordinate plane. On the coordinate plane, the quadrants are labeled __________________________.When we move for a rotation, a positive rotation moves _____________________. and a negative rotation moves ________________.There are __________ in a full rotation.There are __________ in a half rotation.There are __________ in a quarter rotation.-3809990Rules for rotation Clockwise 90 () (x,y)→ __________ counterclockwise 90 () same as ____________Clockwise 180 () (x,y)→__________ counterclockwise 180 () same as ___________Clockwise 270 () (x.y) →__________ counterclockwise 270 () same as ___________Example 1 : Draw the image after a rotation 90 degrees clockwise 340042528575MLJKM’L’J’K’MM’LL’JJ’KK’Example 2: Draw the image after a rotation of 180 degrees clockwise 34112200ABCDA’B’C’D’AA’BB’CC’DD’Example 3: Draw the image after a rotation of 270 degrees clockwise 3067050287020Triangle XYZTriangle X’Y’Z’X(1,3)X’Y(1,6)Y’Z(6,3)Z’Example 4: On the coordinate plane below, graph triangle ECS. Then draw the image of the triangle after . Label your image E’C’S’.4105275247650Triangle ECSTriangle E’C’S’E(-1,-2)E’C(-3,-6)C’S(-6,-2)S’Example 5: Draw the image of WXYZ after a R-270 34099509525RECTANGLEWXYZRECTANGLEW’X’Y’Z’WW’XX’YY’ZZ’For example 6 and example 7 tell if the statement is true of false(Example 6) Seahorse 2 is a 90 degree clockwise (Example 7) Polygon A'B'C'D' is a 180 degree rotation of seahorse 1.counterclockwise rotation of polygon ABCD 3124200247650ROTATION SYMMETRY If you can rotate a figure around a center point by dewer than 360 degrees and the figure appears _______, then the figure has _______________. The point around which you rotate is called the ___________________, and the smallest angle you need to turn is called the _________________. A full turn is 360 degrees, this figure could turn 5 times and look just like the original shape. To find the smallest angle of rotation you divide 360 by 5, therefore the smallest angle of rotation of this shape is 72 degrees.You try finding the smallest angle of rotation on the next 3 figures: We found out above the smallest angle of rotation for a 5 pointed star was 72 degrees. What if I asked what is the angle of rotation from A to C? You would have to make 2, 72 degree turns making the angle of rotation from A to C 144 degrees. 4413052171450You try: What is the angle of rotation from F to B?What is the angle of rotation from A to C?354330026670095250276225DILATIONSThe notation for Dilations looks like: , where k is called the ____________ ______________ .The value for k tells you what to ______________ the x and y coordinates by to get to your image. The rule a dilation with a scale factor, k, is: (x,y)→ (______, ______).EXAMPLE 1: has coordinates . Graph under and state the coordinates of 3333750400050EXAMPLE 2: has coordinates . Graph under and state the coordinates of 162877528575 EXAMPLE 3: Find the coordinates of P’ if P(4, -8) under each of the following dilations: (b) (c) Example 4: Find the scale factor for the following figures. The dashed figure is the dilation (image). 0273685Example 5 ISOMETRIESReflectionsTranslationsRotationsDilationsIsometry: yes or noIsometry: yes or noIsometry: yes or noIsometry: yes or noProperties preserved:1.2.3.4.5.Properties preserved:1.2.3.4.5.Properties preserved:1.2.3.4.5.Properties preserved:1.2.3.4._______not the same Notation: Notation: Notation: Notation: Example 1: Which of the following transformations represents an isometry? Example 2: Which of the following transformations represents an isometry? ................
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