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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 340 · 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.How far is the point (3, 4) from the origin (0, 0)? (a) 6 (b) 5 (c) 25 (d) 7
  2. 2.What is the midpoint of the line joining (1, 9) and (5, 7)? (a) (6, 16) (b) (3, 8) (c) (8, 3) (d) (2, 1)
  3. 3.How far is the point (12, 16) from the origin (0, 0)? (a) 400 (b) 21 (c) 28 (d) 20
  4. 4.In which quadrant does the point (−5, −3) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  5. 5.In which quadrant does the point (8, 2) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  6. 6.What is the distance between the points (4, 6) and (12, 21)? (a) 23 (b) 18 (c) 17 (d) 289
  7. 7.What is the distance between the points (0, 19) and (5, 7)? (a) 17 (b) 14 (c) 13 (d) 169
  8. 8.What is the distance between the points (7, 24) and (14, 0)? (a) 625 (b) 31 (c) 25 (d) 26
  9. 9.What is the distance between the points (0, 7) and (8, 22)? (a) 17 (b) 289 (c) 18 (d) 23
  10. 10.How far is the point (16, 12) from the origin (0, 0)? (a) 28 (b) 20 (c) 400 (d) 21
  11. 11.How far is the point (24, 7) from the origin (0, 0)? (a) 31 (b) 26 (c) 625 (d) 25
  12. 12.How far is the point (12, 5) from the origin (0, 0)? (a) 169 (b) 13 (c) 17 (d) 14
  13. 13.What is the distance between the points (6, 8) and (13, 32)? (a) 25 (b) 625 (c) 26 (d) 31
  14. 14.In which quadrant does the point (5, −5) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  15. 15.What is the distance between the points (0, 3) and (9, 15)? (a) 15 (b) 225 (c) 16 (d) 21
  16. 16.What is the distance between the points (8, 6) and (16, 21)? (a) 289 (b) 18 (c) 17 (d) 23
  17. 17.In which quadrant does the point (−5, −2) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  18. 18.What is the distance between the points (2, 29) and (9, 5)? (a) 625 (b) 31 (c) 26 (d) 25
  19. 19.What is the midpoint of the line joining (4, 0) and (8, 2)? (a) (6, 1) (b) (1, 6) (c) (12, 2) (d) (2, 1)
  20. 20.What is the distance between the points (8, 16) and (17, 4)? (a) 15 (b) 21 (c) 16 (d) 225
  21. 21.What is the midpoint of the line joining (8, 10) and (10, 18)? (a) (18, 28) (b) (9, 14) (c) (14, 9) (d) (1, 4)
  22. 22.In which quadrant does the point (6, 3) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  23. 23.How far is the point (5, 12) from the origin (0, 0)? (a) 14 (b) 13 (c) 17 (d) 169
  24. 24.What is the midpoint of the line joining (0, 20) and (8, 8)? (a) (4, 6) (b) (4, 14) (c) (8, 28) (d) (14, 4)
  25. 25.What is the distance between the points (6, 14) and (14, 8)? (a) 14 (b) 10 (c) 11 (d) 100
  26. 26.What is the midpoint of the line joining (8, 9) and (10, 19)? (a) (18, 28) (b) (1, 5) (c) (14, 9) (d) (9, 14)
  27. 27.In which quadrant does the point (1, −7) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
  28. 28.What is the midpoint of the line joining (10, 10) and (22, 18)? (a) (16, 14) (b) (32, 28) (c) (14, 16) (d) (6, 4)
  29. 29.What is the midpoint of the line joining (7, 4) and (15, 8)? (a) (22, 12) (b) (4, 2) (c) (6, 11) (d) (11, 6)
  30. 30.What is the midpoint of the line joining (9, 8) and (11, 10)? (a) (9, 10) (b) (10, 9) (c) (20, 18) (d) (1, 1)
  31. 31.What is the midpoint of the line joining (3, 10) and (11, 22)? (a) (7, 16) (b) (14, 32) (c) (4, 6) (d) (16, 7)
  32. 32.In which quadrant does the point (5, 8) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  33. 33.What is the distance between the points (3, 3) and (11, 18)? (a) 23 (b) 289 (c) 17 (d) 18
  34. 34.In which quadrant does the point (3, 3) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  35. 35.In which quadrant does the point (−4, 9) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  36. 36.In which quadrant does the point (−9, 5) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  37. 37.What is the distance between the points (4, 7) and (16, 12)? (a) 17 (b) 14 (c) 13 (d) 169
  38. 38.What is the distance between the points (6, 6) and (30, 13)? (a) 625 (b) 26 (c) 25 (d) 31
  39. 39.How far is the point (7, 24) from the origin (0, 0)? (a) 625 (b) 31 (c) 26 (d) 25
  40. 40.What is the midpoint of the line joining (2, 15) and (6, 3)? (a) (8, 18) (b) (4, 9) (c) (2, 6) (d) (9, 4)

Answer key

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

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