TRANSFORMATION BOOK. Name:

Transcription

1 TRANSFORMATION BOOK Name:

2 Pg. TRANSLATION NOTES: You are going to Translate point A to point A. First graph the point (-,) and label it A. Now graph the point (,) and label it A. SYMMETRY ASSIGNMENT: Pg. Write out how ou could describe the movement from A A. How do the coordinates from A change when the go to A? Fill in the blanks: ( -, ) ( - +, + ) Translation: A : You are going to translate a whole triangle: Graph and label the points A (-,), B (-, ), and C (-, ) Now graph and label the points A (,), B (-, ), C (, 0) Write out how ou could describe the translation of Δ ABC to Δ A B C : How do the coordinates from the points in Δ ABC change when the get translated to Δ A B C? Place the letters into the following categories; list them in ever categor the belong. Reflection Smmetr- Horizontal Line of Smmetr Reflection Smmetr- Vertical Line of Smmetr Rotational Smmetr

3 Pg. MCAS PROBLEMS: ) Which of the following pictures appears to have rotational smmetr? A. C. Pg. Now ou will translate Δ XYZ, where X (-, ), Y (-, -), Z (0, -). First graph and label Δ XYZ. Now translate Δ XYZ Δ X Y Z b the rule: add to the value, and subtract from the value. This is written as: (, ) ( +, ). B. D. Graph and label Δ X Y Z b the rule (, ) ( +, ) Write the points for Δ X Y Z : X (, ) Y (, ) Z (, ) Did the shape of the triangle change? ) Which of the following figures has 90 degree rotational smmetr? A. C. Now ou will translate Δ QRS, where Q (, -), R (-, 0), S (, -). First graph and label Δ QRS. Now translate Δ QRS Δ Q R S b the rule: subtract from the value, and add to the value. B. D. Graph and label Δ Q R S b the rule Fill in the blanks for this translation: (, ) (, ) Write the points for Δ Q R S :Q (, ) R (, ) S (, ) Did the shape of the triangle change?

4 Pg. REVIEW: How can ou prove that the triangles are the same? Pg. 0 SYMMETRY: The simplest smmetr is (sometimes called Line Smmetr or Mirror Smmetr). It is eas to see, because one half is the reflection of the other half. With, sometimes called Point Smmetr, the image is rotated around a central point so that it appears or more times. How man lines of smmetr does a regular heagon have? Sketch the smmetr lines on the figure below. How man lines of smmetr does a rectangle have? What about rotational smmetr?

5 Pg. 9 ROTATION ASSIGNMENT: ) Describe how ou could move shape to eactl match shape b using series of transformations? Pg. TRANSLATION ASSIGNMENT: ) Using words, describe the translation that would be made b the rule : (, ) (, + ) ) Using points, find the translation that would be made b the rule : (, ) ( + 9, ) on A(, - ) B(, ) and C(-, ) ) Determine the transformation that produced the following image: F' H' D O D' H F ) If I were to ask ou to translate Δ LMN Δ L M N b the rule: (, ) (, + ), and L is at ( ab,, ) M is at (, cd ) and N is at (, e f ), how would ou write the coordinates for Δ L M N? L (, ) ) Draw the final image created b rotating triangle RST 90 counterclockwise about the origin M (, ) N (, ) ) Using words, make up a translation. ) What are the coordinates of (-, ) under a 0 counterclockwise rotation about the origin? ) What are the coordinates of (, ) under a 90 clockwise rotation about the origin? Write this translation as a mapping/rule. (, ) (, ) Pick points X (, ) Y (, ) Z (, ). Find X (, ) Y (, ) Z (, ).

6 Pg. PROBLEMS: ) ΔABC is translated unit right and units up. Draw the image ΔA B C. What are the coordinates of: A (, -) A B (, 0) B C (, -) C The diagram below shows HIJ and its image HIJ after a single transformation. Which of the following describes the transformation? A. reflection over the -ais B. reflection over the -ais C. rotation 90 clockwise about the origin D. rotation 0 clockwise about the origin Pg. H' H J' J I' I 0 ΔABC ΔA B C As a rule this translation could be written as (, ) ( +, + ). ) ) Describe the translation. L L' As a rule this translation could be written as A' (, ) (, ). P A P' Look up K L M N from pg. 0 K (, ) L (, ) M (, ) N (, ) (, )K (, )N (, )M Quadrilateral K L M N will be rotated 90 clockwise about point M to create quadrilateral K L M N. Find the coordinate of the following: K (, ) L (, ) M (, ) N (, ) 9 L(, ) 9

7 Pg. MCAS PROBLEMS: Point P(, ) and point Q(, ) are plotted on the coordinate grid below P Q 9 0 Pg. VOCABULARY: A transformation is a change in the,, or of a figure. A translation is a transformation which each point of a figure the same and in the same. The resulting figure after a transformation is called the of the original figure. Point P is rotated 0 clockwise about point Q. What are the coordinates of the image of point P after this rotation? A. (, ) B. (, ) C. (, 0) D. (9, ) Y(, ) X(, ) 9 X' (, ) Y' (, ) Which of the following describes the transformation? MCAS PROBLEM: Quadrilateral KLMN is shown on the coordinate grid below (, )K (, )N (, )M 9 L(, ) 9 A. rotation 90 clockwise about the origin B. translation units to the right C. reflection over the -ais D. reflection over the -ais Cop the coordinate grid and quadrilateral KLMN eactl as shown onto the grid in our Student Answer Booklet. Quadrilateral KLMN will be translated 9 units up. a. On our grid, draw quadrilateral KLMN, the image of quadrilateral KLMN after it has been translated 9 units up. Be sure to label the vertices.

8 Pg. REFLECTION NOTES: A reflection is a transformation which the figure over a. This line is called the. Eample : ΔABC is being reflected over the -ais. Draw and label the image ΔA B C. R ais : ΔABC ΔA B C Organize our results from PG. in the table. Starting Point A (, ) B (, ) C (, 0) 90 Rotation 0 Rotation 0 Rotation Pg. 0 Rotation What are the coordinates of: A A B B C C Write a general rule for an -ais reflection:(, ) (, ). Complete each rule for finding the image of an point (, ) under the given rotation. a) 90 rotation about the origin: R O,90 : (, ) (, ) Eample : ΔABC is being reflected over the -ais. Draw and label the image ΔA B C. R ais : ΔABC ΔA B C What are the coordinates of: A B C A B C Write a general rule for an -ais reflection:(, ) (, ). b) 0 rotation about the origin: R O,0 : (, ) (, ) c) 0 rotation about the origin: R O,0 : (, ) (, ) d) 0 rotation about the origin: R O,0 : (, ) (, )

9 Pg. EXAMPLES: Triangle ABC is labeled on our graph below. a) Rotate Triangle ABC, 90 o counterclockwise. Label the REVIEW: ) Points: Pg. triangle A B C. Line: b) Rotate Triangle ABC, 0 o counterclockwise. Label the triangle A B C. Slope: ) Points: c) Rotate Triangle ABC, 0 o counterclockwise. Label the triangle A B C. Line: Slope: ) Points: Line: Slope: Points: Line: Slope:

10 Pg. 9 EXAMPLES: Find the reflection of the quadrilateral WXYZ across the dotted line. What is the equation of the dotted line? Label the image W X Y Z. X Pg. ROTATION NOTES: A rotation is a transformation which the figure about a. This point is called the ; for most rotations it will be the but it can be other points. Positive rotations alwas turn W Z Y QuadrantII (.,+) QuadrantI (+,+) ΔABC is being reflected over the line =. Draw and label the image ΔA B C. R = : ΔABC ΔA B C What are the coordinates of: A A B B C C Write a general rule for a = reflection:(, ) (, ). QuadrantIII (.,.) QuadrantIV (+,.)

11 Pg. PROBLEMS: ) ΔEFG if E(-, ), F(, ) and G(, - ) reflected over the - ais. Notation: Points: E F G Graph: MCAS PROBLEMS: ) Look up K L M N from pg. K (, ) L (, ) M (, ) N (, ) (, )K (, )N (, )M L(, ) 9 Pg. 0 Quadrilateral KLMN will be reflected over the -ais. b. On our grid, draw quadrilateral KLMN, the image of quadrilateral KLMN after it has been reflected over the -ais. Be sure to label the vertices. ΔE F G if E F G reflected over the - ais. Notation: Points: E F G Add these points to the graph above. What do ou notice? ) MCE_Transformations.eps B Common On a coordinate grid, triangle PQR is translated units up and then reflected over the -ais to form triangle P Q R. Which diagram could show triangle PQR, and the location of triangle P Q R after the transformations? A. Q P 0 Q' R R' P' C. Q P 0 R P' R' Q'

12 Pg. B. Q P 0 R P' R' Q' D. R' Q P P' 0 Q' R REFLECTION ASSIGNMENT: ) Pg. ) Quadrilateral EFGH is shown on the coordinate grid below. II 0 F E G III IV H The quadrilateral will be reflected over the -ais. The reflected image will then be translated units left and units up. In which of the following quadrants will the final reflected and translated image lie? A. I and II B. II and III C. II and IV D. III and IV I Describe how ou could move shape to eactl match shape b using one translation and one reflection. ) Below shows the coordinates of triangle PQR. P (-, ) P Q (-, ) Q R (-, ) R Fill in the coordinates of P, Q, and R after a reflection over the -ais. On the grid below, draw triangle PQR and triangle P Q R