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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 809 · 40 questions
TalentJR

How to solve it (Across, up, Pythagoras): Distance: across = difference of the x values, up = difference of the y values; distance = √(across² + up²). Midpoint = ((x₁ + x₂) ÷ 2, (y₁ + y₂) ÷ 2). Quadrants by signs: (+, +) first, (−, +) second, (−, −) third, (+, −) fourth.

NameDateTime takenScore ___ / 40
  1. 1.What is the midpoint of the line joining (9, 10) and (11, 6)? (a) (10, 8) (b) (8, 10) (c) (20, 16) (d) (1, 2)
  2. 2.What is the midpoint of the line joining (8, 8) and (10, 10)? (a) (18, 18) (b) (10, 9) (c) (9, 9) (d) (1, 1)
  3. 3.How far is the point (5, 12) from the origin (0, 0)? (a) 169 (b) 17 (c) 13 (d) 14
  4. 4.In which quadrant does the point (3, 3) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  5. 5.What is the midpoint of the line joining (8, 2) and (16, 0)? (a) (12, 1) (b) (1, 12) (c) (4, 1) (d) (24, 2)
  6. 6.What is the distance between the points (1, 6) and (9, 0)? (a) 10 (b) 11 (c) 100 (d) 14
  7. 7.How far is the point (9, 12) from the origin (0, 0)? (a) 21 (b) 16 (c) 225 (d) 15
  8. 8.What is the distance between the points (3, 18) and (15, 2)? (a) 20 (b) 400 (c) 21 (d) 28
  9. 9.What is the midpoint of the line joining (10, 20) and (22, 10)? (a) (6, 5) (b) (15, 16) (c) (16, 15) (d) (32, 30)
  10. 10.What is the midpoint of the line joining (0, 4) and (8, 10)? (a) (8, 14) (b) (4, 3) (c) (4, 7) (d) (7, 4)
  11. 11.How far is the point (4, 3) from the origin (0, 0)? (a) 5 (b) 7 (c) 6 (d) 25
  12. 12.In which quadrant does the point (5, −1) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  13. 13.What is the midpoint of the line joining (10, 18) and (20, 8)? (a) (30, 26) (b) (13, 15) (c) (5, 5) (d) (15, 13)
  14. 14.What is the midpoint of the line joining (8, 0) and (16, 4)? (a) (24, 4) (b) (4, 2) (c) (12, 2) (d) (2, 12)
  15. 15.What is the distance between the points (4, 9) and (16, 4)? (a) 17 (b) 169 (c) 13 (d) 14
  16. 16.What is the distance between the points (4, 6) and (7, 2)? (a) 7 (b) 6 (c) 25 (d) 5
  17. 17.How far is the point (16, 12) from the origin (0, 0)? (a) 28 (b) 21 (c) 20 (d) 400
  18. 18.What is the midpoint of the line joining (4, 10) and (14, 18)? (a) (18, 28) (b) (5, 4) (c) (14, 9) (d) (9, 14)
  19. 19.How far is the point (12, 5) from the origin (0, 0)? (a) 169 (b) 17 (c) 14 (d) 13
  20. 20.What is the distance between the points (7, 0) and (19, 16)? (a) 28 (b) 20 (c) 21 (d) 400
  21. 21.How far is the point (6, 8) from the origin (0, 0)? (a) 100 (b) 14 (c) 10 (d) 11
  22. 22.In which quadrant does the point (1, 6) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  23. 23.What is the distance between the points (3, 9) and (15, 18)? (a) 21 (b) 15 (c) 225 (d) 16
  24. 24.What is the distance between the points (8, 14) and (14, 6)? (a) 10 (b) 100 (c) 14 (d) 11
  25. 25.What is the midpoint of the line joining (5, 9) and (9, 19)? (a) (14, 7) (b) (7, 14) (c) (2, 5) (d) (14, 28)
  26. 26.In which quadrant does the point (3, 2) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  27. 27.How far is the point (12, 16) from the origin (0, 0)? (a) 28 (b) 20 (c) 21 (d) 400
  28. 28.What is the distance between the points (0, 7) and (24, 0)? (a) 625 (b) 26 (c) 31 (d) 25
  29. 29.How far is the point (8, 15) from the origin (0, 0)? (a) 18 (b) 289 (c) 17 (d) 23
  30. 30.In which quadrant does the point (−4, 7) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  31. 31.What is the distance between the points (0, 18) and (8, 3)? (a) 23 (b) 289 (c) 18 (d) 17
  32. 32.What is the distance between the points (3, 13) and (6, 9)? (a) 7 (b) 6 (c) 5 (d) 25
  33. 33.What is the midpoint of the line joining (5, 12) and (7, 2)? (a) (6, 7) (b) (1, 5) (c) (7, 6) (d) (12, 14)
  34. 34.What is the distance between the points (6, 12) and (22, 0)? (a) 400 (b) 21 (c) 28 (d) 20
  35. 35.In which quadrant does the point (−3, −7) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  36. 36.What is the distance between the points (2, 12) and (10, 6)? (a) 11 (b) 100 (c) 10 (d) 14
  37. 37.What is the distance between the points (7, 14) and (13, 6)? (a) 11 (b) 14 (c) 100 (d) 10
  38. 38.How far is the point (12, 9) from the origin (0, 0)? (a) 21 (b) 15 (c) 225 (d) 16
  39. 39.What is the distance between the points (9, 19) and (17, 4)? (a) 289 (b) 23 (c) 18 (d) 17
  40. 40.What is the distance between the points (2, 9) and (8, 17)? (a) 10 (b) 11 (c) 100 (d) 14

Answer key

  1. (10, 8)
  2. (9, 9)
  3. 13
  4. First quadrant
  5. (12, 1)
  6. 10
  7. 15
  8. 20
  9. (16, 15)
  10. (4, 7)
  11. 5
  12. Fourth quadrant
  13. (15, 13)
  14. (12, 2)
  15. 13
  16. 5
  17. 20
  18. (9, 14)
  19. 13
  20. 20
  21. 10
  22. First quadrant
  23. 15
  24. 10
  25. (7, 14)
  26. First quadrant
  27. 20
  28. 25
  29. 17
  30. Second quadrant
  31. 17
  32. 5
  33. (6, 7)
  34. 20
  35. Third quadrant
  36. 10
  37. 10
  38. 15
  39. 17
  40. 10

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