The Point Defined | | | | 1. | A(2,1), B( “1, “3), C( “3,0), D(0,3), E(3, “3) | | | | | 2. | The answer is shown in Figure 1.21. Figure 1.21. Graph of points A through E. | | | | | 3. | ( “2,1, “4) | | | | | 4. | (2,3,2) | The Line Defined | | | | 1. | Yes | | | | | 2. | Yes | | | | | 3. | Yes | | | | | 4. | No | | | | | 5. | The answer is shown in Figure 1.22. Figure 1.22. Graph of x “ 2y = 0. | | | | | 6. | The answer is shown in Figure 1.23. Figure 1.23. Graph of “3x + y = 4. | | | | | 7. | The answer is shown in Figure 1.24. Figure 1.24. Graph of x = 1. | Properties of Lines | | | | 1. | m = “2 | | | | | 2. | m = “2 | | | | | 3. | m = ½ | | | | | 4. | m = 3 | | | | | 5. | m = 3/2 | | | | | 6. | m = undefined | | | | | 7. | m = ½ | | | | | 8. | m = 0 | | | | | 9. | They are parallel. | | | | | 10. | Vertical | | | | | 11. | Horizontal | | | | | 12. | m = “2/3 | | | | | 13. | m = 1/5 | | | | | 14. | m = 0 | | | | | 15. | m = “1 | | | | | 16. | ( y “10) = “2( x ) or y = “2 x + 10 | | | | | 17. | ( y “5) = “2( x “3) or y = “2 x + 11 | | | | | 18. | ( y +1) = ½( x “2) or y = ½ x “ 2 | | | | | 19. | ( y “4) = 3( x “1) or y = 3 x + 1 | | | | | 20. | point <2,0, “1> and vector <1,4,6> | | | | | 21. | point < “3,1,5> and vector <3,7, “7> | Applications in Collision Detection | | | | 1. | m 1 = “1, b 1 = 7, m 2 = 1/3 , b 2 = 2/3 ; one solution | | | | | 2. | m 1 = 1/3 , b 1 = 2, m 2 = 1/3 , b 2 = “2; zero solutions | | | | | 3. | m 1 = “ ¼, b 1 = 2, m 2 = “ ¼, b 2 = 2; infinite solutions | | | | | 4. | m 1 = 1, b 1 = “5, m 2 = “5, b 2 = 0; one solution | | | | | 5. | m 1 = “ 1/3 , b 1 = “ 1/3 , m 2 = “ 1/3 , b 2 = “ 5/6 ; zero solutions | | | | | 6. | m 1 = 3/5 , b 1 = , m 2 = “ 3/5 , b 2 = ; one solution | |