Reflections. Reflections in the Coordinate Plane. Translations Battleship Warm Up
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1 Reflections Translations Battleship Warm Up Phase : Position our battleships on our gameboard according to the following specifications: - Aircraft Carrier - rectangle, area of units, nd quadrant onl - Battleship - square, area of units, both st and th quadrant - Submarine - parallelogram area of units, rd quadrant - Destroer - trapezoid, area of units, ou choose the quadrant Phase : Write the coordinates of each battleship in both our gameboard AND our opponent s gameboard. Phase : The enem is getting closer. Time to move. You must move all of our boats at least once. Write all as Translation Rules using the correct notation. Redraw our moved boats in another color on our board! Write the rules in our board area and our opponent's. Example of Translation Rule: Aircraft carrier (x, ) (x -, + ) Phase : Hand our answer ke to Ms. Hahn and then switch with our opponent gameboards with our partner. Work to find each other s boat locations after the translations. Check our game board with me when ou think ou sunk all their ships. First person to find each other s ships wins! Your gameboard will be graded as an assignment grade! If ou win our duo, ou ll win a prize! Reflections in the Coordinate Plane A reflection is a transformation which the figure over a. This line is called the.
2 EXAMPLE ΔABC is being reflected over the x- axis. Draw and label the image ΔA B C. We can use an arrow to describe this reflection. ΔABC à ΔA B C What are the coordinates of: A à A B à B C à C Write a general rule for an x- axis reflection: (x, ) à (, ). EXAMPLE ΔABC is reflected over the - axis. Draw the image ΔA B C. What are the coordinates of: A à A B à B C à C Write a general rule for a - axis reflection: (x, ) à (, ). Tell me more about the relationship between the preimage and the image. Are the congruent or similar? Explain how ou know.
3 EXAMPLE a) Draw ΔABC which has coordinates A(, 0), B(, - ), and C(, - ). b) Draw the image ΔA B C after a reflection of ΔABC over = x. c) List the coordinates of A B C. A (, 0) à A B (, - ) à B C (, - ) à C Write a general rule for an = x reflection: x (x, ) à (, ). EXAMPLE a) Draw ΔABC which has coordinates A(0,), B(,), and C(,). b) Draw the image ΔA B C after a reflection of ΔABC over = - x. c) List the coordinates of A B C. A (0, ) à A B (, ) à B C (, ) à C x Write a general rule for an = - x reflection: (x, ) à (, ).
4 EXAMPLE a) Draw ΔABC which has coordinates A(-, ), B(, ), and C(, ). b) Draw the image ΔA B C after a reflection of ΔABC over =. c) List the coordinates of A B C. A (-, - ) à A B (, ) à B C (, ) à C x *** You can reflect over an line, but the most important ones are listed as follows: Reflection Line Rule x- axis - axis = x = - x Reflections Practice. Draw the line of reflection which caused rectangle KLMN to reflect onto rectangle K L M N. What is the equation of the line of reflection? L K K' L' x M N N' M'
5 . Draw the line of reflection which caused triangle ABC to reflect onto triangle A B C. What is the equation of the line of reflection? A B C x A' C' B'. Find the reflection of the triangle HOT over the x- axis. O Write the coordinates of H O T. Is the image similar or congruent? How do ou know? H x T. 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 W x Z Y
6 . Quadrilateral CDEF is plotted on the grid below. On the graph, draw the reflection of polgon CDEF over the line = x. Label the image C D E F. Now create polgon C D E F b translating polgon C D E F three units to the left and up two units. What will be the coordinates of point C? Answer. a) Draw ΔJKL which has coordinates J (0,), K (,), and L (,). b) Draw the image ΔJ K L after a reflection of ΔJKL over the x- axis. c) List the coordinates of J K L. J (0, ) à J K (, ) à K L (, ) à L d) Draw the image ΔJ K L after a reflection of ΔJ K L over the - axis. e) List the coordinates of J K L. J à J x K à K L à L f) Describe a different combination of two reflections that would move ΔJKL to ΔJ K L. g) Is this new image congruent or similar to the original figure?
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8 th Grade Name Date Period Study Guide - Chapter 6 1) Label each quadrant with I, II, III, or IV. 2) Use your knowledge of rotations to name the quadrant that each point below will land in after the rotation
Practice For use with pages
9. For use with pages 598 605 Use the translation (, ) ( 6, 3).. What is the image of (3, )?. What is the image of (4, )? 3. What is the preimage of 9(, 7)? 4. What is the preimage of 9(3, )? The vertices