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: With words 2 left and 3 up. Coordinate notation (x, y)  (x + 1, y – 3) Vector notation <-2, 4> Vector – a direction with a length.

Translate each of the following by their indicated translation 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’ B’ A B A B

Translate each of the following by their indicated translation 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 Complete the statement using the description of the translation. In the description, points (0, 2) and (8, 5) are two vertices of a pentagon. If (0, 2) maps onto (0, 0), then (8, 5) maps onto (____, ____). If (0, 2) maps onto (____, ____) , then (8, 5) maps onto (3, 7). If (0, 2) maps onto (-3, -5) , 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) What is the image of (5, 3)? What is the image of (-1, -2)? 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, 3 -2, 1 2, 1 -3, 1 3, 1 -3, 5 3, 5 x- axis reflection -2, 3 -2, -3 -2, 1 -2, -1 -3, 1 -3,- 1 -3, 5 -3, -5

J( , )  J’( , ) K( , )  K’( , ) L( , ) L’( , ) (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’( , )

A( , )  S’( , )   B( , )  B’( , ) C( , ) C’( , )

Q( , )  Q’( , ) R( , )  R’( , ) S( , ) S’( , ) 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. x = 4 2. y = x 3. y = -6 4. y = -x 5. y = 2x – 4 A vertical line Undefined slope Goes through the x-axis at 4 A slope of 1 Y- intercept of 0 Diagonal line 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 A slope of 2 Y-intercept of -4

A reflection over the line x = 1 Q’ R’ (3, 2) P’ (8, 1) Q’ (6, 4) R’ P’

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 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.

Rotations are congruent 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. 180° Rotations are congruent 270° 90° II I III IV - 90° - 270° - 180°

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. 135° 150° 165° 180°

Quadrilateral A’B’C’D’ is the image of quadrilateral ABCD under a rotation about the origin, (0, 0). Determine the angle of rotation. −90° −30° 30° 90°

Quadrilateral A’B’C’D’ is the image of quadrilateral ABCD under a rotation about the origin, (0, 0). Determine the angle of rotation. −45° −15° 15° 45°

Determine the angle of rotation for the image under a rotation about point P or Q. −75° −45° 45° 75°

Determine the angle of rotation for the image under a rotation about point P or Q. −125° 125° 165° −165°

Determine the angle of rotation for the image under a rotation about point P or Q. −105° −150° 105° 150°

Rotations are congruent A transformation that turns a figure a certain amount of degrees around a fixed point.   _________________ A( )  A’( ) B( )  B’( ) C( )  C’( ) Rotations are congruent 90° Rotation A’ B’ C’ 2 , 5 -5 , 2 C 1 , 3 -3 , 1 5 , 3 -3 , 5

Rotations are congruent   _________________ A( )  A’( ) B( )  B’( ) C( )  C’( ) Rotations are congruent 180° Rotation 2 , 5 -2 , -5 C 1 , 3 - 1, -3 5 , 3 -5 , -3 A’ B’ C’

Rotations are congruent   _________________ A( )  A’( ) B( )  B’( ) C( )  C’( ) Rotations are congruent 270° Rotation 2 , 5 5 , -2 C 1 , 3 3 , -1 5 , 3 A’ B’ C’ 3 , -5

Rotations 90° or -270° 180° 270° or -90° 360° (– y, x ) (– x, – y )

Rotate coordinates first, then draw. Rotations Rotate coordinates first, then draw. 𝑅 (𝑂,90°) ∆𝐽𝐾𝐿 Rule: J ( , )  J’ ( , ) K ( , )  K’ ( , ) L ( , )  L’ ( , ) K’ (– y, x ) L’ J’ 1 3 -3 1 3 -2 2 3 1 -2 2 1

Rotations 𝑅 (𝑂,180°) ∆𝐴𝐵𝐶 Rule: A ( , )  A’ ( , ) B ( , )  B’ ( , ) C’ A’ 𝑅 (𝑂,180°) ∆𝐴𝐵𝐶 Rule: A ( , )  A’ ( , ) B ( , )  B’ ( , ) C ( , )  C’ ( , ) B’ (– x, -y ) -5 -6 5 6 -3 -2 3 2 -1 -6 1 6

Rotations Q ( , )  Q’ ( , ) R ( , )  R’ ( , ) S ( , )  S’ ( , ) Rule: Rotation: -5 2 5 -2 -2 5 2 -5 -2 1 2 -1 (– x, y ) 180°

What about other degrees? What are some degrees that points could be rotated in the following pictures? E A B C D R F G H

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

Dilations Concept 39