12/11/17, 4:35 PM 6.5.5 Journal: Point on a Circle Journal Riley Klingelberg Mathematics II Sem 2 (S4288622) Points possible: 20 Date: ____________ Scenario: Pony Ride Instructions: View the video found on page 1 of this journal activity. Using the information provided in the video, answer the questions below. Show your work for all calculations The Students' Conjectures: The students are running a pony ride business. They are trying to decide where to stake the pony so that the pony can't reach the fence or trample a rose bush. Complete the table below to summarize what you know about each student's conjecture: (2 points, 1 point for each row of the chart) Classmate Conjecture David Joy Analyze the Conjecture: What are the arguments against each student's plan? (1 point) http://acecontent.apexlearning.com/online/int_math_II_cc_sem_2_2013/Unit_6/Lesson_5/Activity_58344/printables/Journal955069.htm Page 1 of 6 12/11/17, 4:35 PM Analyze the Data: Suppose that this grid represents the customer's yard. The bottom left corner is the origin point, (0,0), and the x and y axes represent the two fences. The rose bush is at point (16, 18). Use this graph for questions 2 through 12. David's Plan: 2. What are the coordinates of the point where David wants to put the stake? Draw this point on the graph. (1 point) 3. If they stake the pony where David wants, what is the equation of the circle that represents the pony's path? (2 points) 4. Sketch the equation of this circle onto the graph. (1 point) http://acecontent.apexlearning.com/online/int_math_II_cc_sem_2_2013/Unit_6/Lesson_5/Activity_58344/printables/Journal955069.htm Page 2 of 6 12/11/17, 4:35 PM 5. Does the rose bush lie on this circle? Use algebra to show your answer. (2 points) Joy's Plan 6. What are the coordinates of the point where Joy wants to put the stake? Draw this point on your graph. (1 point) 7. If they stake the pony where Joy wants, what is the equation of the circle that represents the pony's path? (2 points) 8. Sketch the equation of this circle onto the graph. (1 point) http://acecontent.apexlearning.com/online/int_math_II_cc_sem_2_2013/Unit_6/Lesson_5/Activity_58344/printables/Journal955069.htm Page 3 of 6 12/11/17, 4:35 PM 9. Does the rose bush lie on this circle? Use algebra to show your answer. (2 points) 10. If the pony is staked at the point (8,8), will the pony's path be interrupted by the fence? Use algebra to explain your answer. (1 point) Making a Decision 11. Who was correct? Is either point (10,10) or (8,8) a good place to stake the pony? (1 point) http://acecontent.apexlearning.com/online/int_math_II_cc_sem_2_2013/Unit_6/Lesson_5/Activity_58344/printables/Journal955069.htm Page 4 of 6 12/11/17, 4:35 PM 12. Consider the circle with equation (x - 12) 2+(y - 12) 2=100. a) What is the center of this circle? (1 point) b) Would this circle work for the pony's path? Why or why not? Use algebra to show your answer. (2 points) http://acecontent.apexlearning.com/online/int_math_II_cc_sem_2_2013/Unit_6/Lesson_5/Activity_58344/printables/Journal955069.htm Page 5 of 6 12/11/17, 4:35 PM Copyright 2013 Apex Learning Inc. (See Terms of Use at www.apexvs.com/TermsOfUse) http://acecontent.apexlearning.com/online/int_math_II_cc_sem_2_2013/Unit_6/Lesson_5/Activity_58344/printables/Journal955069.htm Page 6 of 6