Midpoint and Distance



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. (–4, 10) and (4, –5) 4. (–7, –4) and (2, 8)

5. (–1, 2) and (5, 4) 6. (2, 10) and (10, 2)

7. ( , 1) and (– , ) 8. (– , – ) and (– , – )

9. (–36, –18) and (48, –72)

10 Find x so that the distance between the points is 13. a) (1, 2) and (x, –10); b)  and (x, 5).

11. Find y so that the distance between the points is 17. a) (0, 0) and (8, y); b) (–8, 4) and (7, y).

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).

13. Find the perpendicular bisector of the line that connects the two points (1, 1) and .

14. Find the perpendicular bisector of the line that connects the two points (–4, 2) and .

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, –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)

Find the center and radius of each of the following circles:

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

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 =

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