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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 469 · 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 (−3, 2) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  2. 2.In which quadrant does the point (3, 7) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  3. 3.What is the midpoint of the line joining (6, 7) and (10, 5)? (a) (16, 12) (b) (2, 1) (c) (8, 6) (d) (6, 8)
  4. 4.What is the distance between the points (7, 3) and (31, 10)? (a) 26 (b) 25 (c) 31 (d) 625
  5. 5.What is the midpoint of the line joining (7, 10) and (9, 16)? (a) (1, 3) (b) (13, 8) (c) (8, 13) (d) (16, 26)
  6. 6.In which quadrant does the point (3, −7) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  7. 7.How far is the point (3, 4) from the origin (0, 0)? (a) 7 (b) 25 (c) 6 (d) 5
  8. 8.In which quadrant does the point (−3, 7) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  9. 9.What is the distance between the points (1, 11) and (13, 2)? (a) 21 (b) 225 (c) 15 (d) 16
  10. 10.What is the midpoint of the line joining (4, 11) and (6, 9)? (a) (10, 5) (b) (10, 20) (c) (5, 10) (d) (1, 1)
  11. 11.How far is the point (12, 16) from the origin (0, 0)? (a) 21 (b) 20 (c) 28 (d) 400
  12. 12.How far is the point (6, 8) from the origin (0, 0)? (a) 10 (b) 11 (c) 100 (d) 14
  13. 13.In which quadrant does the point (−7, −6) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  14. 14.What is the distance between the points (7, 4) and (23, 16)? (a) 28 (b) 400 (c) 21 (d) 20
  15. 15.How far is the point (5, 12) from the origin (0, 0)? (a) 17 (b) 14 (c) 169 (d) 13
  16. 16.What is the midpoint of the line joining (0, 1) and (4, 11)? (a) (2, 6) (b) (6, 2) (c) (4, 12) (d) (2, 5)
  17. 17.How far is the point (7, 24) from the origin (0, 0)? (a) 31 (b) 25 (c) 26 (d) 625
  18. 18.What is the distance between the points (9, 9) and (17, 24)? (a) 23 (b) 17 (c) 18 (d) 289
  19. 19.What is the midpoint of the line joining (8, 12) and (20, 8)? (a) (6, 2) (b) (28, 20) (c) (10, 14) (d) (14, 10)
  20. 20.In which quadrant does the point (−9, −6) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  21. 21.In which quadrant does the point (−2, 4) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  22. 22.What is the distance between the points (4, 1) and (28, 8)? (a) 26 (b) 31 (c) 25 (d) 625
  23. 23.How far is the point (12, 5) from the origin (0, 0)? (a) 17 (b) 14 (c) 169 (d) 13
  24. 24.What is the midpoint of the line joining (1, 10) and (13, 2)? (a) (14, 12) (b) (6, 4) (c) (7, 6) (d) (6, 7)
  25. 25.What is the midpoint of the line joining (8, 7) and (10, 19)? (a) (9, 13) (b) (13, 9) (c) (18, 26) (d) (1, 6)
  26. 26.In which quadrant does the point (−9, −5) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
  27. 27.What is the midpoint of the line joining (9, 19) and (15, 9)? (a) (3, 5) (b) (24, 28) (c) (14, 12) (d) (12, 14)
  28. 28.What is the distance between the points (7, 5) and (23, 17)? (a) 21 (b) 20 (c) 28 (d) 400
  29. 29.What is the distance between the points (2, 16) and (7, 4)? (a) 14 (b) 169 (c) 17 (d) 13
  30. 30.What is the midpoint of the line joining (8, 3) and (16, 1)? (a) (12, 2) (b) (24, 4) (c) (4, 1) (d) (2, 12)
  31. 31.What is the distance between the points (1, 9) and (4, 5)? (a) 5 (b) 6 (c) 7 (d) 25
  32. 32.In which quadrant does the point (−3, −2) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  33. 33.What is the distance between the points (2, 19) and (18, 7)? (a) 20 (b) 21 (c) 400 (d) 28
  34. 34.How far is the point (24, 7) from the origin (0, 0)? (a) 31 (b) 625 (c) 26 (d) 25
  35. 35.What is the distance between the points (7, 9) and (15, 24)? (a) 17 (b) 18 (c) 23 (d) 289
  36. 36.What is the distance between the points (8, 14) and (20, 5)? (a) 21 (b) 225 (c) 15 (d) 16
  37. 37.What is the midpoint of the line joining (8, 0) and (16, 2)? (a) (12, 1) (b) (24, 2) (c) (4, 1) (d) (1, 12)
  38. 38.What is the distance between the points (3, 9) and (11, 24)? (a) 18 (b) 23 (c) 289 (d) 17
  39. 39.What is the midpoint of the line joining (0, 6) and (12, 16)? (a) (6, 5) (b) (11, 6) (c) (12, 22) (d) (6, 11)
  40. 40.How far is the point (15, 8) from the origin (0, 0)? (a) 289 (b) 17 (c) 18 (d) 23

Answer key

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

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