Benchmark Test 5. Translations. More Copy if needed

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1 enchmark LESSON Tests More op if needed enchmark Test 5 Translations Use the diagram for Exercises and x. Write a rule for the translation of to Write a rule for the translation of 999 back to.. } PQ is a line segment with endpoints P(, ) and Q(, 5). The image } P9Q9 is a line segment with endpoints P9(, ) and Q9(9, 0). Which of the following is a rule for the translation?. (x, ) (x 5, 5). (x, ) (x 5, 5). (x, ) (x 5, 5). (x, ) (x 5, 5). Name the vector and write its component form a. See graph. 6b. 6c. 5. What is the component form of the vector that describes the translation of the point P(6, ) to P9(, )?. k8, 7l. k8, 7l. k8, 7l. k8, 7l 6. a. Translate the triangle units up and units left. Graph the image using prime notation. 8 6 Q P R x 6 8 opright b Mcougal Littell, a division of Houghton Mifflin ompan. b. Find the coordinates of the vertices P9, Q9, and R9 after the translation. c. Write the component form of the vector that describes the translation.

2 enchmark Test 5 continued 7. Which matrix is the translation matrix used to translate a triangle 5 units right and units down? F. G F 5 5 5G G. F 5. F The matrix F 0 represents. Find the image matrix G that represents the translation of units left and units up. Reflections, Rotations, and ilations 9. What are coordinates of the image of the point (, 5) when it is reflected in the line 5?. (, 5). (, ). (0, 5). (, ) 0. The point J(, ) is reflected in the line x 5. It is reflected again in the line x 5. What are the coordinates of the resulting point?. (, ). (, ). (, ). (0, ). The endpoints of } are (, ) and (, ). Graph the line segment and then reflect the segment in the line 5x. 5G See graph. a. b. c.. opright b Mcougal Littell, a division of Houghton Mifflin ompan. x. The vertices of VWX are V(, ), W(, ), and X(6, ). a. Write the polgon matrix. b. Write the reflection matrix used to reflect the polgon in the x-axis. c. Write the image matrix of the triangle reflected in the x-axis.. Which matrix is used to reflect a polgon in the -axis?. F 0. F 0 0 G. 0G F 0 0. G F 0 0G

3 enchmark LESSON Tests More op if needed enchmark Test 5 continued. The vertices of PQR are P(, ), Q(, ), and R(, ). Graph the triangle and then rotate the triangle 70 about the origin. x. See graph. 5a. 5b. 5c The vertices of VWX are V(6, ), W(, 9), and X(, ). a. Write the polgon matrix. b. Write the image matrix of the triangle rotated 90 counterclockwise about the origin. c. Write the image matrix of the triangle rotated 80 counterclockwise about the origin. 6. Which matrix is used to rotate a polgon 70 counterclockwise?. F G F. 0G F 0. 0 G F 0 0G The matrix F represents. Find the image matrix G that represents the dilation of the triangle centered at the origin with the scale factor k 5 }. 8. dilation with its center at the origin maps (9, ) to 9(5, 0). What is the scale factor?. k 5 }. k 5 5 }. k 5 5 }. k The vertices of LMN are L(, ), M(, ), and N(, ). Graph LMN and its image after the glide reflection. Translation: (x, ) (x, 6) Reflection: in the -axis See graph. opright b Mcougal Littell, a division of Houghton Mifflin ompan. x

4 enchmark Test 5 continued 0. The endpoints of } PQ are P(, ) and Q(, ). What are the coordinates of the endpoints after a rotation of 90 about the origin, followed b a reflection in the line 5 x?. P0(, ), Q0(, ). P0(, ), Q0(, ). P0(, ), Q0(, ). P0(, ), Q0(, ). The vertices of are (, 6), (6, ) and N(, 7). Find the coordinates of the vertices after a composition of the transformations listed. Translation: (x, ) (x, ) Rotation: 80 about the origin Reflection: in the x-axis Smmetr. How man lines of smmetr does a regular hexagon have? How man lines of smmetr does the object have? opright b Mcougal Littell, a division of Houghton Mifflin ompan.. escribe the line smmetr and rotational smmetr of a regular nonagon. 5. Identif the line smmetr and rotational smmetr of the figure below.. 6 lines of smmetr, no rotational smmetr. lines of smmetr, 60 rotational smmetr. 6 lines of smmetr, 0 rotational smmetr. lines of smmetr, 0 rotational smmetr 5

5 enchmark LESSON Tests More op if needed enchmark Test 5 continued 6. raw a pentagon with one line of smmetr and no rotational smmetr. If not possible, write not possible. ircles and Special Segments and Lines Use the diagram for Exercises See sketch E F. 7. Name a chord of ( that is not a diameter. 8. Name a diameter of (. 9. Name a radius of (. 0. Which term best radius. chord. tangent. secant. Which term best describes?. point of tangenc. center. common tangent. radius. In the diagram, is a point of tangenc. Find the radius r of (.. What is the value of x? r x r 0 6 x x opright b Mcougal Littell, a division of Houghton Mifflin ompan. 6

6 enchmark Test 5 continued Use the diagram for Exercises 8. } is a diameter of. E Find m. 5. Find m E. 6. Find m E. 7. What is m E? What is m E? Use the diagram for Exercises 9. } } E F.. opright b Mcougal Littell, a division of Houghton Mifflin ompan. 9. If m 5 0, find m. 0. If m 5 0, what is m? Suppose E 5 x and F 5 5x 8. Find the value of x.. Suppose 5 6 and E 5. What is F? Use the diagram for Exercises and. E F. Suppose 5 6x and F 5 x. Find the value of x.. Suppose m 5 (x 5) and m 5 (5x 5). What is m?

7 enchmark Test 5 continued enchmark LESSON Tests More op if needed 5. Find ST and QT. R Q x 5 T x P S Find the value of x. 9. x 50. x 7. What is the value of x? Round to the nearest tenth. 9 x ngle Relationships in ircles Use the diagram for Exercises Q 8 R U 5 S T 8. Find m RST. 9. Find m STQ. 50. What is m QS? opright b Mcougal Littell, a division of Houghton Mifflin ompan. 8

8 enchmark Test 5 continued Use the diagram for Exercises 5 and 5. x ( 5) 8 5. Find the value of x. 5. What is the value of? Use the diagram for Exercises 5 and opright b Mcougal Littell, a division of Houghton Mifflin ompan. 5. Find m. 5. What is m? What is the value of x? 7 x Write the standard equation of the circle with center (, ) and radius The point (, ) is on a circle whose center is (, ). Write the standard equation of the circle. 9