Math Quiz Review 2.1 Answer Key

Advanced Math Quiz 2.1 & 2.3 Review Name DISTANCE FORMULA: MIDPOINT FORMULA: Find the distance between the set of points 1. (−3, 4) and (7, 2) 2. (−2, −6) and (3, −4) 1.)_________________ 2.)_________________ Find the midpoint between the set of points 3. (−3, 4) and (7, 2) 4. (4, −2) and (7, 2) 3.)________________ 4.)________________ 5. (𝑥, −2𝑥) and (5𝑥, 4𝑥) 6. (3𝑥, 4𝑥) and (−6𝑥, 9𝑥) 5.)________________ 6.)________________ SLOPE INTERCEPT FORM: Graph the linear function using the slope and 𝒚-intercept. 7. 𝑦 = − 2 𝑥 3 +5 𝑚 =_____ 𝑏 = _____ 8. 1 𝑦 2 =𝑥−3 𝑚 =_____ 𝑏 = _____ Graph the linear function using the slope and 𝒚-intercept. 9. 3𝑥 + 4𝑦 = 16 𝑚 =_____ 𝑏 = _____ 10. 2𝑥 − 3𝑦 = 9 𝑚 =_____ 𝑏 = _____ Find the slope of the line through the given points. 11. (3, −7), (−4, 10) 12. (−2, −5), (4, −6) 11.)______________ 12.)______________ Find the equation of the indicated line in slope-intercept form. 13. 𝑦-intercept = (0, −4), slope = 2 3 14. 𝑦-intercept = (0, 2), slope = 5 13.)______________ 14.)______________ 1 15. Through (4, −6), slope = 2 16. Through (−5, −1), slope = −3 15.)______________ 16.)______________ 17. Through (5, −6) and (2, −8) 18. Through (−5, 6) and (−3, −4) 17.)______________ 18.)______________ Find the equation of the line, in slope-intercept form, that satisfies the given conditions. 19. The graph is parallel to the graph of 𝑦 = −𝑥 + 1 and passes through the point whose coordinates are (−2, 4). 20. The graph is parallel to the graph of 𝑦 = whose coordinates are (−3, −5). 2 𝑥 3 19.)______________ − 1 and passes through the point 21. The graph is parallel to the graph of 𝑥 + 3𝑦 = 4 and passes through the point whose coordinates are (−3, −1). 20.)______________ 21.)______________ 22. The graph is perpendicular to the graph of 𝑦 = −𝑥 + 3 and passes through the point whose coordinates are (−5, 2). 22.)______________ 23. The graph is perpendicular to the graph of 3𝑥 − 2𝑦 = 5 and passes through the point whose coordinates are (−3, 4). 23.)______________ 24. The graph is perpendicular to the graph of 5𝑥 − 𝑦 = 2 and passes through the point whose coordinates are (10, −2). 24.)______________ EQUATION FOR A CIRCLE: Determine the center and radius of the circle with the given equation. 25. 𝑥 2 + 𝑦 2 = 81 26. 𝑥 2 + 𝑦 2 = 48 25. Center:________________ 25. Radius:________________ 26. Center:________________ 26. Radius:________________ 27. (𝑥 − 3)2 + (𝑦 + 5)2 = 24 28. (𝑥 + 8)2 + (𝑦 − 9)2 = 27 27. Center:________________ 27. Radius:________________ 28. Center:________________ 28. Radius:________________ Find an equation of a circle that satisfies the given conditions. Write your answer in standard form. 29. Center (−3, 2) and radius 6 30. Center (4, −6) and radius √7 29.)_______________________ 30.)_______________________ 31. Center (0, 0), passing through (3, 4) 31.)_______________________ 32. Center (1, −5), passing through (−2, 4) 32.)_______________________ ANSWERS: 2.1 & 2.3 1. 2√26 2. √29 5. (3𝑥, 𝑥) 6. ( 7. 𝑚: − ; 𝑏: 5 or (0, 5) 9. 𝑚: − 4; 𝑏: 4 or (0, 4) 11. − 15. 𝑦= (2, 3) 8. 𝑚: 2; 𝑏: − 6 or (0, − 6) 10. 𝑚: 13. 𝑦= 2 𝑥 3 −4 3 1 6 17. 𝑦= 2 𝑥 3 − 21. 𝑦 = − 3𝑥 − 2 2 ; 3 ( 2 , 0) 14. 𝑦 = 5𝑥 + 2 18. 𝑦 = −5𝑥 − 19 22. 𝑦 = 𝑥+7 𝑏: −3 or (0, −3) 12. − −8 16. 𝑦 = −3𝑥 − 16 19. 𝑦 = −𝑥 + 2 20. 𝑦= 23. 𝑦 = − 3𝑥 + 2 24. 𝑦 = − 5𝑥 25. Center : (0, 0) Radius : 9 26. Center : (0, 0) Radius : 4√3 27. Center : (3, − 5) Radius : 2√6 28. Center : (− 8, 9) Radius : 3√3 29. (𝑥 + 3)2 + (𝑦 − 2)2 = 36 30. (𝑥 − 4)2 + (𝑦 + 6)2 = 7 31. 𝑥 2 + 𝑦 2 = 25 32. (𝑥 − 1)2 + (𝑦 + 5)2 = 90 1 𝑥 2 11 4. − 3𝑥 13𝑥 , 2 ) 2 2 3 17 7 3. 2 𝑥 3 2 −3 28 3 1 1