Translations Concept 36 Translation slide the moving of
- Slides: 49
Translations Concept 36
Translation – slide – the moving of an object in one or more directions. Pre-image – the original object before any transformation has happened. - ex. Quadrilateral ABCD Image – the result after a transformation has taken place. - ex. Quadrilateral A’B’C’D’
Ways to describe or write a translation: 1) With words a. 2 left and 3 up. 2) Coordinate notation a. (x, y) (x + 1, y – 3) 3) Vector notation a. <-2, 4> Vector – a direction with a length.
Translate each of the following by their indicated translation. Use the pre-image of AB A(-3, 2) and B(2, -1) 1. up 3 and left 4 2. (x, y) (x – 4, y) A’ B’ A’ A A B’ B B
Translate each of the following by their indicated translation. Use the pre-image of AB A(-3, 2) and B(2, -1) 3. <3, 4> A’ B’ A B
Use coordinate notation to describe the translation. 4. 6 units to the right and 1 unit down 5. 7 units to the left and 1 unit up 6. 8 units down and 5 units to the left
Complete the statement using the description of the translation. In the description, points (0, 2) and (8, 5) are two vertices of a pentagon. 7. If (0, 2) maps onto (0, 0), then (8, 5) maps onto (____, ____). 8. If (0, 2) maps onto (____, ____) , then (8, 5) maps onto (3, 7). 9. If (0, 2) maps onto (-3, -5) , then (8, 5) maps onto (____, ____). 10. If (0, 2) maps onto (____, ____) , then (8, 5) maps onto (0, 0).
Consider the translation that is defined by (x, y) (x +12, y – 7) 11. What is the image of (5, 3)? 12. What is the image of (-1, -2)? 13. What is the preimage of (0, 6)?
Draw the image after each indicated translation. 14. (x, y) (x + 4, y + 1)
Draw the image after each indicated translation. 15. (x, y) (x – 2, y)
Reflections CONCEPT 37
Vocabulary Reflection – the mirror image of all sets of points in an object over a specific line. Reflections using a geomirror.
Reflections using transparency paper. y- axis reflection -2, 3 -2, 1 -3, 1 2, 1 3, 1 -3, 5 x- axis reflection -2, 3 -2, -3 -2, 1 -3, 1 -2, -1 -3, - 1 -3, 5 -3, -5
(x, -y) (-x, -y) The negative sign means the opposite of the x or y value List the ordered pairs for each pre-image. Then find the ordered pairs for the image with the described reflection J( , ) J’( K( , ) K’( L( , ) L’( , ) , , ) )
List the ordered pairs and decide what transformation took place. Q( , ) Q’( R( , ) R’( S( , ) S’( , ) , , ) )
Reflections over other lines than the axis. Describe each line. 1. x = 4 2. y = x A vertical line Undefined slope Goes through the x-axis at 4 A slope of 1 Y- intercept of 0 Diagonal line 3. y = -6 4. y = -x A horizontal line Slope of zero Goes through the y-axis at -6 A slope of -1 Y-intercept of 0 Diagonal line from the left top 5. y = 2 x – 4 A slope of 2 Y-intercept of -4
A reflection over the line x = 1 Q’ R’ P’ R’ (3, 2) P’ (8, 1) Q’ (6, 4)
A reflection over the line y = -1 Q’ (3, 2) R’ (-2, -5) S’ (6, -8) T’ (4, -4) T’ Q’ R’ S’
A reflection over the line y = 4
A reflection over the line y = -x A’ (-6, -1) P’ (1, -2) Q’ (-1, 6) A’ C’ B’
A reflection over the line y = 2
A reflection over the line y = x
Rotations CONCEPT 38
Rotations A transformation that turns a figure a certain amount of degrees around a fixed point.
A transformation that turns a figure a certain amount of degrees around a fixed point. Quadrants run counterclockwise, rotations will run counterclockwise as positive degrees. II I III IV Rotations are congruent Rotations
Determine which point is the image of the indicated point by the degree indicated around the center. Point P rotated by -90° Point Q rotated by -30° Point P rotated by 135°
Quadrilateral A’B’C’D’ is the image of quadrilateral ABCD under a rotation about the origin, (0, 0). Determine the angle of rotation.
Quadrilateral A’B’C’D’ is the image of quadrilateral ABCD under a rotation about the origin, (0, 0). Determine the angle of rotation.
Quadrilateral A’B’C’D’ is the image of quadrilateral ABCD under a rotation about the origin, (0, 0). Determine the angle of rotation.
Determine the angle of rotation for the image under a rotation about point P or Q.
Determine the angle of rotation for the image under a rotation about point P or Q.
Determine the angle of rotation for the image under a rotation about point P or Q.
A transformation that turns a figure a certain amount of degrees around a fixed point. C’ C A’ B’ ________ _ 2, 5 -5 , 2 A( 1 , 3 ) A’(-3 , 1 ) B( 5 , 3 ) B’(-3 , 5 ) C( ) C’( ) Rotations are congruent Rotations
B’ C’ A’ Rotations are congruent C ________ _ 2, 5 -2 , -5 A( 1 , 3 ) A’(- 1, -3 ) B( 5 , 3 ) B’(-5 , -3 ) C( ) C’( )
B’ A’ C’ Rotations are congruent C ________ _ 2, 5 5 , -2 A( 1 , 3 ) A’(3 , -1 ) B( 5 , 3 ) B’(3 , -5 ) C( ) C’( )
Rotations 90° or 270° (– y, x ) 180° 270° or -90° (– x, – y ) ( y, – x ) 360° ( x, y )
Rotations Rotate coordinates first, then draw. K’ J’ L’ (– y, x ) 1 3 3 -2 1 -2 -3 1 2 3 2 1
Rotations C’ A’ B’ (– x, -y ) -5 -6 -3 -2 -1 -6 5 6 3 2 1 6
Rotations Q ( -5 , 2 ) Q’ ( 5 , -2 ) R (-2 , 5) R’ ( 2 , -5) S ( -2 , 1) S’ ( 2 , -1) Rule: (– x, y ) Rotation: 180°
What about other degrees? What are some degrees that points could be rotated in the following pictures? B A C H R D G F E
What about other degrees? What are some degrees that points could be rotated in the following pictures?
Exit Slip Get an index card from the purple drawer. Write your name and answer the following: 1. If A is (3, 4), what is A’ after a 180º rotation? 2. Is -270º a CC or C rotation? 3. If B is (3, 4), what is B’ after a -90º rotation? Green: Got it! Blue: Need More Help
Rotations
Rotations
Rotations
DILATI ONS Concept 39
- Heel and toe step
- What process occurs
- Translate
- Voice translation-rule
- Linear parent function
- Noun phrase example
- Four types of transformations
- Translation slide
- Slide divide method
- Examples of equivalence in translation
- Composée de deux translations
- Translation reflection rotation dilation
- Translations of trigonometric graphs
- Show ip nat translations
- Translation reflection rotation
- Abowd and beale model
- Lesson 9-2 translations
- Lesson 9-2 translations
- Relation de chasles
- 9-2 translations
- 9-2 translations
- 6-5 practice translations of sine and cosine functions
- Reflections translations and rotations
- Identify reflections, rotations, and translations
- Translations reflections and rotations are all known as
- Translations in art
- Translations of quadratic functions
- What are the properties of translations
- Lesson 9-2 translations
- How to verify a congruence transformation
- Transformation of absolute value functions
- Translation et vecteur
- Translations brian friel summary
- Lesson 1 translations
- Turkish bible translations
- Back translations
- Transformations of linear and absolute value functions
- Translate the following sentences
- Spivak the politics of translation
- Algebraic translations
- Journalistic document translations
- Journalistic document translations
- Translations rotations reflections and dilations
- Translations of shapes
- Composée de deux translations
- Hát kết hợp bộ gõ cơ thể
- Lp html
- Bổ thể
- Tỉ lệ cơ thể trẻ em
- Gấu đi như thế nào