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Math A Lab – Transformational Geometry Part A What is the image of point 2,5 under the translation that shifts x, y to x 3, y 2 ? What is the image of point 4,7 under the translation that shifts x, y to x 1, y 4 ? What is the image of point 3,2 under the translation that shifts x, y to x 1, y 5 ? Part B State which transformation of ABC to A' B' C ' is shown in the accompanying diagram. State which transformation of ABC to A' B' C ' is shown in the accompanying diagram. State which transformation of ABC to A' B' C ' is shown in the accompanying diagram. Part C When the point 2,5 is reflected in the x-axis, what are the coordinates of its image? When the point 6,3 is reflected in the y-axis, what are the coordinates of its image? When the point 1,4 is reflected in the line y x , what are the coordinates of its image? Part D How many line symmetries does the following figure have? How many line symmetries does the following figure have? How many line symmetries does the following figure have? Part E (True or False) A Translation always produces an image that is congruent to the original figure. (True or False) A Dilation always produces an image that is congruent to the original figure. (True or False) A Reflection always produces an image that is congruent to the original figure. Part F Helen is using a capital H in an art design. How many line symmetries and point symmetries does the H have? Lines of symmetry Points of symmetry Helen is using a capital S in an art design. How many line symmetries and point symmetries does the S have? Helen is using a capital X in an art design. How many line symmetries and point symmetries does the X have? Lines of symmetry Lines of symmetry Points of symmetry Points of symmetry Part G Which of the following have point symmetry? M A T H Which of the following have point symmetry? W O N B Which of the following have point symmetry? Z E D S PART H In the accompanying diagram, ABC is congruent to A' B' C ' . Which transformation is represented by A' B' C ' ? In the accompanying diagram, ABC is congruent to A' B' C ' . Which transformation is represented by A' B' C ' ? In the accompanying diagram, ABC is similar but not congruent to A' B' C ' . Which transformation is represented by A' B' C ' ? PART I If x 2 and y 1 , which point on the accompanying set of axes represents the translation x, y x 2, y 3 ? If x 2 and y 1 , which point on the set of axes above represents the translation x, y x 2, y 3 ? If x 2 and y 1 , which point on the set of axes above represents the translation x, y x 2, y 3 ? PART J The accompanying diagram shows a transformation. Which transformation performed on figure 1 resulted in figure 2? The accompanying diagram shows a transformation. Which transformation performed on figure 1 resulted in figure 2? The accompanying diagram shows a transformation. Which transformation performed on figure 1 resulted in figure 2? PART K In the accompanying diagram, which transformation changes the solid-line parabola to the dotted-line parabola? In the accompanying diagram, which transformation changes the solid-line parabola to the dotted-line parabola? In the accompanying diagram, which transformation changes the solid-line parabola to the dotted-line parabola? PART L Draw all the symmetry lines on the accompanying figure. Draw all the symmetry lines on the accompanying figure. Draw all the symmetry lines on the accompanying figure. PART M The coordinates of the endpoints of AB are A (0,6) and B (4,6) . Graph and state the coordinates of A’ and B’, the image of A and B after AB is reflected in the x-axis. The coordinates of the endpoints of AB are A (1,2) and B (5,7) . Graph and state the coordinates of A’ and B’, the image of A and B after AB is reflected in the y-axis. The coordinates of the endpoints of AB are A (0,4) and B (1,6) . Graph and state the coordinates of A’ and B’, the image of A and B after AB is reflected in the line y x . PART N The coordinates of the endpoints of AB are A 2,6 and B 4,2 . Is the image A' ' B' ' the same if it is reflected in the x-axis, then dilated by 1 2 as the image is if it is dilated by 1 2 , then reflected in the xaxis? Justify your answer. The coordinates of the endpoints of AB are A 3,5 and B 1,2 . Is the image A' ' B' ' the same if it is reflected in the y-axis, then dilated by 2 as the image is if it is dilated by 2, then reflected in the x-axis? Justify your answer. The coordinates of the endpoints of AB are A 0,4 and B 2,6 . Is the image A' ' B' ' the same if it is reflected in the y-axis, then dilated by 1 2 as the image is if it is dilated by 1 2 , then reflected in the x-axis? Justify your answer. PART O On the accompanying set of axes, graph ABC with coordinates A 1,2 , B 0,6 , and C 5,4 . Then graph A' B' C ' , the image of ABC after a dilation of 2. On a sheet of graph paper,, graph ABC with coordinates A 3,2 , B 0,4 , and C 6,3 . Then graph A' B' C ' , the image of ABC after a translation x, y x 3, y 2 On a sheet of graph paper, graph ABC with coordinates A 1,2 , B 0,6 , and C 5,4 . Then graph A' B' C ' , the image of ABC after a rotation of 90 degrees about the origin counterclockwise. PART P Triangle SUN has coordinates S 0,6 , U 3,5 , and N 3,0 . On the accompanying grid, draw and label SUN . Then, graph and state the coordinates of S' U' N' , the image of SUN after a reflection in the y-axis. Triangle XYZ has coordinates X 2,5 , Y 4,2 , and Z 1,4 . On a sheet of graph paper, draw and label XYZ . Then, graph and state the coordinates of X ' Y' Z' , the image of XYZ after a reflection in the x-axis. Triangle ABC has coordinates A 0,6 , B 3,5 , and C 3,0 . On a sheet of graph paper, draw and label ABC . Then, graph and state the coordinates of A' B' C' , the image of ABC after a reflection in the line y x . PART Q On the accompanying grid, draw and label quadrilateral ABCD with points A 1,2 , B 6,1 , C 7,6 , and D 3,7 . On the same set of axes, plot and label quadrilateral A’B’C’D’, the reflection of quadrilateral ABCD in the y-axis. Determine the area, in square units, of quadrilateral A’B’C’D’. On a sheet of graph paper, draw and label quadrilateral QRST with points Q 1,1 , R 3,5 , S 9,5 , and T 7,1 . On the same set of axes, plot and label quadrilateral Q’R’S’T’, the reflection of quadrilateral QRST in the x-axis. Determine the area, in square units, of quadrilateral Q’R’S’T’. On a sheet of graph paper, draw and label quadrilateral MATH with points M 3,2 , A 0,3 , T 2,1 , and H 4,1 . On the same set of axes, plot and label quadrilateral M’A’T’H’, the reflection of quadrilateral MATH in the yaxis. Determine the area, in square units, of quadrilateral M’A’T’H’.