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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 459 · 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.In which quadrant does the point (−9, 6) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  2. 2.What is the distance between the points (7, 3) and (11, 6)? (a) 5 (b) 25 (c) 7 (d) 6
  3. 3.How far is the point (12, 9) from the origin (0, 0)? (a) 21 (b) 15 (c) 225 (d) 16
  4. 4.In which quadrant does the point (−6, −9) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  5. 5.In which quadrant does the point (9, 6) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  6. 6.What is the midpoint of the line joining (5, 8) and (9, 18)? (a) (14, 26) (b) (13, 7) (c) (7, 13) (d) (2, 5)
  7. 7.What is the distance between the points (0, 20) and (16, 8)? (a) 28 (b) 400 (c) 21 (d) 20
  8. 8.How far is the point (24, 7) from the origin (0, 0)? (a) 25 (b) 26 (c) 31 (d) 625
  9. 9.What is the midpoint of the line joining (3, 5) and (7, 9)? (a) (2, 2) (b) (7, 5) (c) (5, 7) (d) (10, 14)
  10. 10.What is the distance between the points (6, 9) and (18, 0)? (a) 21 (b) 16 (c) 225 (d) 15
  11. 11.In which quadrant does the point (1, 8) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  12. 12.What is the distance between the points (2, 7) and (14, 12)? (a) 14 (b) 169 (c) 17 (d) 13
  13. 13.What is the distance between the points (1, 10) and (4, 6)? (a) 25 (b) 6 (c) 5 (d) 7
  14. 14.What is the distance between the points (6, 7) and (18, 16)? (a) 16 (b) 21 (c) 225 (d) 15
  15. 15.In which quadrant does the point (−2, 2) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  16. 16.What is the distance between the points (7, 14) and (12, 2)? (a) 17 (b) 14 (c) 169 (d) 13
  17. 17.How far is the point (16, 12) from the origin (0, 0)? (a) 28 (b) 21 (c) 400 (d) 20
  18. 18.What is the distance between the points (5, 4) and (8, 8)? (a) 7 (b) 25 (c) 5 (d) 6
  19. 19.What is the distance between the points (9, 9) and (33, 2)? (a) 625 (b) 31 (c) 26 (d) 25
  20. 20.What is the distance between the points (8, 4) and (15, 28)? (a) 31 (b) 25 (c) 26 (d) 625
  21. 21.What is the midpoint of the line joining (10, 1) and (12, 3)? (a) (22, 4) (b) (2, 11) (c) (1, 1) (d) (11, 2)
  22. 22.What is the midpoint of the line joining (5, 9) and (9, 19)? (a) (14, 7) (b) (14, 28) (c) (7, 14) (d) (2, 5)
  23. 23.What is the distance between the points (4, 6) and (19, 14)? (a) 23 (b) 18 (c) 17 (d) 289
  24. 24.In which quadrant does the point (−6, −8) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  25. 25.How far is the point (8, 15) from the origin (0, 0)? (a) 289 (b) 17 (c) 23 (d) 18
  26. 26.How far is the point (12, 5) from the origin (0, 0)? (a) 14 (b) 13 (c) 169 (d) 17
  27. 27.How far is the point (7, 24) from the origin (0, 0)? (a) 625 (b) 26 (c) 25 (d) 31
  28. 28.What is the distance between the points (0, 19) and (8, 4)? (a) 23 (b) 18 (c) 289 (d) 17
  29. 29.What is the midpoint of the line joining (10, 3) and (20, 7)? (a) (5, 2) (b) (5, 15) (c) (30, 10) (d) (15, 5)
  30. 30.What is the distance between the points (0, 3) and (12, 12)? (a) 15 (b) 21 (c) 16 (d) 225
  31. 31.In which quadrant does the point (2, −9) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  32. 32.What is the midpoint of the line joining (5, 10) and (11, 0)? (a) (16, 10) (b) (5, 8) (c) (8, 5) (d) (3, 5)
  33. 33.How far is the point (15, 8) from the origin (0, 0)? (a) 289 (b) 18 (c) 23 (d) 17
  34. 34.In which quadrant does the point (−9, −5) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  35. 35.In which quadrant does the point (1, 3) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  36. 36.What is the midpoint of the line joining (10, 5) and (16, 1)? (a) (3, 13) (b) (13, 3) (c) (26, 6) (d) (3, 2)
  37. 37.How far is the point (8, 6) from the origin (0, 0)? (a) 14 (b) 100 (c) 11 (d) 10
  38. 38.What is the midpoint of the line joining (0, 5) and (2, 15)? (a) (10, 1) (b) (1, 10) (c) (1, 5) (d) (2, 20)
  39. 39.In which quadrant does the point (−9, 2) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  40. 40.What is the midpoint of the line joining (4, 4) and (6, 14)? (a) (9, 5) (b) (1, 5) (c) (10, 18) (d) (5, 9)

Answer key

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

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