╨╧рб▒с>■  13■   0                                                                                                                                                                                                                                                                                                                                                                                                                                                ье┴7 Ё┐еbjbjUU " 7|7|е       l       4ЄЄЄЄ 4╘╢6 ╠       xzzz;╡╨Е╨U$К кДy      yр    Оррр    xр xрМрl  l * 2Фr>╟4╛Є фll д0╘l.№ ф.lр44    ┘Midpoint and Distance Find the distance and midpoint of each of the following pairs of points: 1. (1 ,1) and (9, 7) 2. (1, 12) and (6, 0) 3. (Ц4, 10) and (4, Ц5) 4. (Ц7, Ц4) and (2, 8) 5. (Ц1, 2) and (5, 4) 6. (2, 10) and (10, 2) 7. ( eq \f( 1 ,2) , 1) and (Ц  eq \f( 5 ,2) ,  eq \f( 4 ,3) ) 8. (Ц  eq \f( 1 ,3) , Ц  eq \f( 1 ,3) ) and (Ц  eq \f( 1 ,6) , Ц  eq \f( 1 ,2) ) 9. (Ц36, Ц18) and (48, Ц72) 10 Find x so that the distance between the points is 13. a) (1, 2) and (x, Ц10); b)а eq (Ц8,а0) and (x, 5). 11. Find y so that the distance between the points is 17. a) (0, 0) and (8, y); b)а(Ц8,а4) and (7, y). 12. Find a relationship between x and y so that (x, y) is equidistant from the two points: a) (4, Ц1) and (Ц2, 3) b) (3,  eq \f( 5 ,2) ) and (Ц7, 1). 13. Find the perpendicular bisector of the line that connects the two points (1, 1) and  eq (Ц1, 3). 14. Find the perpendicular bisector of the line that connects the two points (Ц4, 2) and  eq (Ц1, 3). Find the standard form of the equation for each of the following circles: 15. Center (0, 0), radius = 3 16. Center (0, 0), radius = 5 17. Center (2, Ц1), radius = 4 18. Center (0,  eq \f( 1 ,3) ), radius =  eq \f( 1 ,3)  19. Center (Ц1, 2), passing through (0, 0) 20. Center (3, Ц2), passing through (Ц1, 1) 21. Endpoints of a diameter are (0, 0) and (6, 8) 22. Endpoints of a diameter are (Ц4, Ц1) and (4, 1) Find the center and radius of each of the following circles: 23. x2 + y2 Ц 2x + 6y + 6 = 0 24. x2 + y2 Ц 2x + 6y Ц 15 = 0 25. x2 + y2 Ц 2x + 6y + 10 = 0 26. 3x2 + 3y2 Ц 6y Ц 1 = 0 27. 2x2 + 2y2 Ц 2x Ц 2y Ц 3 = 0 28. 4x2 + 4y2 Ц 4x + 2y Ц 1 = 0 29. 16x2 + 16y2 + 16x + 40y Ц 7 = 0 30. x2 + y2 Ц 4x + 2y + 3 = 0 Answers 1. 10; (5, 4) 2. 13; (  eq \f( 7 ,2) , 6) 3. 17; (0,  eq \f( 5 ,2) ) 4. 15; (Ц  eq \f( 5 ,2) , 2) 5. 2 eq \r(10 ); (2, 3) 6. 8 eq \r(2 ); (6, 6) 7.  eq \f( \r(82 ) ,3) ; (Ц1,  eq \f( 7 ,6) ) 8.  eq \f( \r(2 ) ,6) ; (Ц  eq \f( 1 ,4) , Ц  eq \f(5, 12 ) ) 9. 6 eq \r(277 ); (6, Ц45) 10. a) Ц4, 6 b) Ц20, 4 11. a) ▒15 b) Ц4, 12 12. a) 3x Ц 2y = 1; b) 80x + 12y = Ц139 13. y = x + 2 14. 3x + y = Ц5 15. x2 + y2 = 9 16. x2 + y2 = 25 17. (x Ц 2)2 + (y + 1)2 = 16 18. x2 + (y Ц  eq \f( 1 ,3) )2 =  eq \f( 1 ,9)  19. (x + 1)2 + (y Ц 2)2 = 5 20. (x Ц 3)2 + (y + 2)2 = 25 21. (x Ц 3)2 + (y Ц 4)2 = 25 22. x2 + y2 = 17 23. (1, Ц3); r = 2 24. (1, Ц3); r = 5 25. Not a circle 26. x2 + (y Ц 1)2 =  eq \f(2,3)  eq \r(3 ) 27. (eq \f( 1 ,2) ,  eq \f( 1 ,2) ); r =  eq \r(2 ) 28. (eq \f( 1 ,2) , Ц  eq \f( 1 ,4) ); r =  eq \f( 3 ,4)  29. ( Ц eq \f( 1 ,2) , Ц  eq \f( 5 ,4) ); r =  eq \f( 3 ,2)  30. 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