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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 960 · 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 (7, 20) and (13, 8)? (a) (3, 6) (b) (10, 14) (c) (14, 10) (d) (20, 28)
  2. 2.How far is the point (5, 12) from the origin (0, 0)? (a) 169 (b) 14 (c) 17 (d) 13
  3. 3.In which quadrant does the point (7, −3) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  4. 4.What is the distance between the points (6, 2) and (15, 14)? (a) 15 (b) 225 (c) 21 (d) 16
  5. 5.What is the distance between the points (9, 16) and (33, 9)? (a) 625 (b) 31 (c) 25 (d) 26
  6. 6.What is the distance between the points (1, 1) and (16, 9)? (a) 23 (b) 18 (c) 17 (d) 289
  7. 7.In which quadrant does the point (5, −3) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  8. 8.In which quadrant does the point (9, 1) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  9. 9.What is the midpoint of the line joining (6, 16) and (14, 4)? (a) (11, 10) (b) (20, 20) (c) (10, 10) (d) (4, 6)
  10. 10.What is the distance between the points (5, 2) and (20, 10)? (a) 23 (b) 17 (c) 289 (d) 18
  11. 11.How far is the point (9, 12) from the origin (0, 0)? (a) 225 (b) 15 (c) 21 (d) 16
  12. 12.In which quadrant does the point (−6, −6) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  13. 13.What is the distance between the points (5, 8) and (14, 20)? (a) 225 (b) 21 (c) 15 (d) 16
  14. 14.How far is the point (12, 16) from the origin (0, 0)? (a) 28 (b) 20 (c) 400 (d) 21
  15. 15.In which quadrant does the point (−7, −7) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  16. 16.What is the distance between the points (2, 16) and (11, 4)? (a) 225 (b) 15 (c) 16 (d) 21
  17. 17.What is the midpoint of the line joining (3, 4) and (13, 2)? (a) (5, 1) (b) (16, 6) (c) (3, 8) (d) (8, 3)
  18. 18.What is the distance between the points (0, 26) and (7, 2)? (a) 31 (b) 25 (c) 26 (d) 625
  19. 19.What is the midpoint of the line joining (2, 10) and (12, 18)? (a) (14, 28) (b) (14, 7) (c) (5, 4) (d) (7, 14)
  20. 20.What is the distance between the points (3, 21) and (12, 9)? (a) 16 (b) 15 (c) 225 (d) 21
  21. 21.What is the distance between the points (9, 22) and (17, 7)? (a) 18 (b) 23 (c) 17 (d) 289
  22. 22.How far is the point (6, 8) from the origin (0, 0)? (a) 100 (b) 14 (c) 11 (d) 10
  23. 23.What is the distance between the points (6, 3) and (14, 9)? (a) 14 (b) 11 (c) 10 (d) 100
  24. 24.In which quadrant does the point (7, 8) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  25. 25.What is the distance between the points (6, 7) and (21, 15)? (a) 289 (b) 18 (c) 17 (d) 23
  26. 26.In which quadrant does the point (−5, 9) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  27. 27.What is the midpoint of the line joining (9, 8) and (11, 2)? (a) (10, 5) (b) (20, 10) (c) (5, 10) (d) (1, 3)
  28. 28.What is the midpoint of the line joining (1, 0) and (11, 8)? (a) (5, 4) (b) (6, 4) (c) (4, 6) (d) (12, 8)
  29. 29.How far is the point (15, 8) from the origin (0, 0)? (a) 289 (b) 18 (c) 23 (d) 17
  30. 30.What is the distance between the points (2, 8) and (17, 16)? (a) 17 (b) 23 (c) 289 (d) 18
  31. 31.What is the midpoint of the line joining (1, 0) and (7, 10)? (a) (5, 4) (b) (3, 5) (c) (4, 5) (d) (8, 10)
  32. 32.What is the distance between the points (9, 7) and (12, 11)? (a) 5 (b) 25 (c) 6 (d) 7
  33. 33.What is the distance between the points (4, 31) and (11, 7)? (a) 625 (b) 25 (c) 26 (d) 31
  34. 34.What is the midpoint of the line joining (6, 1) and (12, 7)? (a) (9, 4) (b) (18, 8) (c) (3, 3) (d) (4, 9)
  35. 35.In which quadrant does the point (−2, −4) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  36. 36.What is the midpoint of the line joining (5, 9) and (15, 7)? (a) (10, 8) (b) (5, 1) (c) (20, 16) (d) (8, 10)
  37. 37.What is the distance between the points (9, 10) and (17, 4)? (a) 10 (b) 14 (c) 11 (d) 100
  38. 38.In which quadrant does the point (−1, −8) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  39. 39.What is the midpoint of the line joining (7, 2) and (9, 12)? (a) (8, 7) (b) (1, 5) (c) (16, 14) (d) (7, 8)
  40. 40.In which quadrant does the point (−2, −5) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant

Answer key

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

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