11X1 T07 03 angle between two lines (2011)

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  • 1. Angle Between Two Lines

2. Angle Between Two Lines y x 3. Angle Between Two Lines y1 x l1 4. Angle Between Two Lines yl1 has slope m1 tan 11 x l1 5. Angle Between Two Lines l y 2 l1 has slope m1 tan 12 1xl1 6. Angle Between Two Lines l y 2 l1 has slope m1 tan 1 l2 has slope m2 tan 22 1xl1 7. Angle Between Two Lines l y 2 l1 has slope m1 tan 1 l2 has slope m2 tan 22 1xl1 8. Angle Between Two Lines l y 2 l1 has slope m1 tan 1 l2 has slope m2 tan 22 11 2 (exterior )xl1 9. Angle Between Two Lines l y 2 l1 has slope m1 tan 1 l2 has slope m2 tan 22 11 2(exterior )x 1 2l1 10. Angle Between Two Lines l y 2l1 has slope m1 tan 1 l2 has slope m2 tan 22 1 1 2(exterior )x 1 2 tan tan 1 2 l1 11. Angle Between Two Lines l y 2 l1 has slope m1 tan 1 l2 has slope m2 tan 22 11 2 (exterior )x 1 2 tan tan 1 2 l1tan 1 tan 2 1 tan 1 tan 2 12. Angle Between Two Lines l y 2 l1 has slope m1 tan 1 l2 has slope m2 tan 22 11 2 (exterior )x 1 2 tan tan 1 2 l1tan 1 tan 2 1 tan 1 tan 2 m1 m2 1 m1m2 13. Angle Between Two Lines l y2 l1 has slope m1 tan 1 l2 has slope m2 tan 221 1 2 (exterior ) x 1 2 tan tan 1 2 l1tan 1 tan 2 1 tan 1 tan 2 m1 m2 1 m1m2The acute angle between two lines with slopes m1 and m2 can befound using; 14. Angle Between Two Lines l y2 l1 has slope m1 tan 1 l2 has slope m2 tan 221 1 2 (exterior ) x 1 2 tan tan 1 2 l1tan 1 tan 2 1 tan 1 tan 2 m1 m2 1 m1m2The acute angle between two lines with slopes m1 and m2 can befound using; m1 m2 tan 1 m1m2 15. 2000 Extension 1 HSC Q1b)e.g. Find the acute angle between the lines 1y 2 x 1 and y x 1 3 16. 2000 Extension 1 HSC Q1b)e.g. Find the acute angle between the lines 1y 2 x 1 and y x 1 3 12 tan 3 1 1 2 3 17. 2000 Extension 1 HSC Q1b)e.g. Find the acute angle between the lines 1y 2 x 1 and y x 1 3 12 tan 3 1 1 2 36 13 2 18. 2000 Extension 1 HSC Q1b)e.g. Find the acute angle between the lines 1y 2 x 1 and y x 1 3 12 tan 3 1 1 2 36 13 21 19. 2000 Extension 1 HSC Q1b)e.g. Find the acute angle between the lines 1y 2 x 1 and y x 1 3 12 tan 3 1 1 2 36 13 21 45 20. 2005 Extension 1 HSC Q1f)(ii) The acute angle between the lines y = 3x + 5 and y = mx + 4 is 45 Find the possible values of m. 21. 2005 Extension 1 HSC Q1f)(ii) The acute angle between the lines y = 3x + 5 and y = mx + 4 is 45 Find the possible values of m.3 mtan 45 1 3m 22. 2005 Extension 1 HSC Q1f)(ii) The acute angle between the lines y = 3x + 5 and y = mx + 4 is 45 Find the possible values of m.3 mtan 45 1 3m3 m1 1 3m 23. 2005 Extension 1 HSC Q1f)(ii) The acute angle between the lines y = 3x + 5 and y = mx + 4 is 45 Find the possible values of m.3 mtan 45 1 3m3 m1 1 3m 1 3m 3 m 24. 2005 Extension 1 HSC Q1f)(ii) The acute angle between the lines y = 3x + 5 and y = mx + 4 is 45 Find the possible values of m.3 mtan 45 1 3m3 m1 1 3m 1 3m 3 m 1 3m 3 m or 1 3m 3 m 25. 2005 Extension 1 HSC Q1f)(ii) The acute angle between the lines y = 3x + 5 and y = mx + 4 is 45 Find the possible values of m.3 mtan 45 1 3m3 m1 1 3m 1 3m 3 m 1 3m 3 m or 1 3m 3 m4m 2 26. 2005 Extension 1 HSC Q1f)(ii) The acute angle between the lines y = 3x + 5 and y = mx + 4 is 45 Find the possible values of m.3 mtan 45 1 3m3 m1 1 3m 1 3m 3 m 1 3m 3 m or 1 3m 3 m4m 2 1 m 2 27. 2005 Extension 1 HSC Q1f)(ii) The acute angle between the lines y = 3x + 5 and y = mx + 4 is 45 Find the possible values of m.3 mtan 45 1 3m3 m1 1 3m 1 3m 3 m 1 3m 3 m or 1 3m 3 m4m 2 1 3m 3 m 1 m 2 28. 2005 Extension 1 HSC Q1f)(ii) The acute angle between the lines y = 3x + 5 and y = mx + 4 is 45 Find the possible values of m.3 mtan 45 1 3m3 m1 1 3m 1 3m 3 m 1 3m 3 m or 1 3m 3 m4m 2 1 3m 3 m 1 m 2m 4 2 29. 2005 Extension 1 HSC Q1f)(ii) The acute angle between the lines y = 3x + 5 and y = mx + 4 is 45 Find the possible values of m.3 mtan 45 1 3m3 m1 1 3m 1 3m 3 m 1 3m 3 m or 1 3m 3 m4m 2 1 3m 3 m 1 m 2m 4 2m 2 30. 2005 Extension 1 HSC Q1f)(ii) The acute angle between the lines y = 3x + 5 and y = mx + 4 is 45 Find the possible values of m. 3 m tan 45 1 3m3 m1 1 3m 1 3m 3 m 1 3m 3 m or 1 3m 3 m4m 2 1 3m 3 m 1 m 2m 4 21 m 2 m or m 22 31. Exercise 14E; 1ac, 2bdf, 4, 7, 8, 10, 11a, 15*