<p> Midpoint and Distance</p><p>Find the distance and midpoint of each of the following pairs of points:</p><p>1. (1 ,1) and (9, 7) 2. (1, 12) and (6, 0)</p><p>3. (–4, 10) and (4, –5) 4. (–7, –4) and (2, 8)</p><p>5. (–1, 2) and (5, 4) 6. (2, 10) and (10, 2)</p><p>7. ( , 1) and (– , ) 8. (– , – ) and (– , – )</p><p>9. (–36, –18) and (48, –72)</p><p>10 Find x so that the distance between the points is 13. a) (1, 2) and (x, –10); b) and (x, 5).</p><p>11. Find y so that the distance between the points is 17. a) (0, 0) and (8, y); b) (–8, 4) and (7, y).</p><p>12. Find a relationship between x and y so that (x, y) is equidistant from the two points: a) (4, –1) and (–2, 3) b) (3, ) and (–7, 1).</p><p>13. Find the perpendicular bisector of the line that connects the two points (1, 1) and .</p><p>14. Find the perpendicular bisector of the line that connects the two points (–4, 2) and .</p><p>Find the standard form of the equation for each of the following circles:</p><p>15. Center (0, 0), radius = 3 16. Center (0, 0), radius = 5 17. Center (2, –1), radius = 4 18. Center (0, ), radius = 19. Center (–1, 2), passing through (0, 0) 20. Center (3, –2), passing through (–1, 1) 21. Endpoints of a diameter are (0, 0) and (6, 8) 22. Endpoints of a diameter are (–4, –1) and (4, 1)</p><p>Find the center and radius of each of the following circles:</p><p>23. x2 + y2 – 2x + 6y + 6 = 0 24. x2 + y2 – 2x + 6y – 15 = 0 25. x2 + y2 – 2x + 6y + 10 = 0 26. 3x2 + 3y2 – 6y – 1 = 0 27. 2x2 + 2y2 – 2x – 2y – 3 = 0 28. 4x2 + 4y2 – 4x + 2y – 1 = 0 29. 16x2 + 16y2 + 16x + 40y – 7 = 0 30. x2 + y2 – 4x + 2y + 3 = 0 Answers</p><p>1. 10; (5, 4) 2. 13; ( , 6) 3. 17; (0, ) 4. 15; (– , 2) 5. 2; (2, 3) 6. 8; (6, 6) 7. ; (–1, ) 8. ; (– , – ) 9. 6; (6, –45) 10. a) –4, 6 b) –20, 4 11. a) ±15 b) –4, 12 12. a) 3x – 2y = 1; b) 80x + 12y = –139 13. y = x + 2 14. 3x + y = –5 15. x2 + y2 = 9 16. x2 + y2 = 25 17. (x – 2)2 + (y + 1)2 = 16 18. x2 + (y – )2 = 19. (x + 1)2 + (y – 2)2 = 5 20. (x – 3)2 + (y + 2)2 = 25 21. (x – 3)2 + (y – 4)2 = 25 22. x2 + y2 = 17 23. (1, –3); r = 2 24. (1, –3); r = 5 25. Not a circle 26. x2 + (y – 1)2 = 27. (, ); r = 28. (, – ); r = 29. ( – , – ); r = 30. (2, –1); r = </p>