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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 962 · 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 (9, 12) from the origin (0, 0)? (a) 16 (b) 15 (c) 225 (d) 21
  2. 2.What is the midpoint of the line joining (2, 13) and (12, 7)? (a) (10, 7) (b) (14, 20) (c) (5, 3) (d) (7, 10)
  3. 3.How far is the point (12, 5) from the origin (0, 0)? (a) 169 (b) 17 (c) 14 (d) 13
  4. 4.What is the midpoint of the line joining (2, 0) and (4, 12)? (a) (1, 6) (b) (6, 3) (c) (6, 12) (d) (3, 6)
  5. 5.What is the distance between the points (0, 13) and (5, 1)? (a) 13 (b) 17 (c) 169 (d) 14
  6. 6.What is the midpoint of the line joining (1, 4) and (3, 10)? (a) (1, 3) (b) (2, 7) (c) (7, 2) (d) (4, 14)
  7. 7.What is the midpoint of the line joining (10, 19) and (12, 7)? (a) (13, 11) (b) (22, 26) (c) (11, 13) (d) (1, 6)
  8. 8.How far is the point (7, 24) from the origin (0, 0)? (a) 26 (b) 25 (c) 31 (d) 625
  9. 9.What is the distance between the points (9, 8) and (14, 20)? (a) 17 (b) 169 (c) 14 (d) 13
  10. 10.In which quadrant does the point (3, −5) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  11. 11.What is the distance between the points (7, 1) and (15, 7)? (a) 11 (b) 10 (c) 14 (d) 100
  12. 12.What is the midpoint of the line joining (7, 7) and (17, 17)? (a) (5, 5) (b) (13, 12) (c) (12, 12) (d) (24, 24)
  13. 13.What is the distance between the points (9, 5) and (24, 13)? (a) 23 (b) 18 (c) 17 (d) 289
  14. 14.In which quadrant does the point (2, 4) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  15. 15.What is the distance between the points (2, 21) and (18, 9)? (a) 20 (b) 28 (c) 400 (d) 21
  16. 16.How far is the point (4, 3) from the origin (0, 0)? (a) 6 (b) 7 (c) 5 (d) 25
  17. 17.What is the distance between the points (3, 6) and (11, 12)? (a) 11 (b) 14 (c) 100 (d) 10
  18. 18.What is the distance between the points (7, 8) and (13, 16)? (a) 10 (b) 14 (c) 11 (d) 100
  19. 19.What is the midpoint of the line joining (3, 7) and (9, 9)? (a) (12, 16) (b) (3, 1) (c) (8, 6) (d) (6, 8)
  20. 20.How far is the point (8, 6) from the origin (0, 0)? (a) 14 (b) 11 (c) 10 (d) 100
  21. 21.How far is the point (6, 8) from the origin (0, 0)? (a) 14 (b) 100 (c) 11 (d) 10
  22. 22.What is the midpoint of the line joining (1, 10) and (7, 8)? (a) (3, 1) (b) (8, 18) (c) (9, 4) (d) (4, 9)
  23. 23.In which quadrant does the point (−5, −9) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  24. 24.What is the distance between the points (6, 1) and (14, 7)? (a) 11 (b) 14 (c) 10 (d) 100
  25. 25.In which quadrant does the point (−4, 2) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  26. 26.In which quadrant does the point (2, −7) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  27. 27.What is the distance between the points (7, 6) and (15, 21)? (a) 18 (b) 289 (c) 23 (d) 17
  28. 28.What is the distance between the points (8, 18) and (20, 9)? (a) 21 (b) 225 (c) 16 (d) 15
  29. 29.What is the midpoint of the line joining (9, 0) and (13, 6)? (a) (11, 3) (b) (2, 3) (c) (22, 6) (d) (3, 11)
  30. 30.What is the midpoint of the line joining (1, 1) and (7, 3)? (a) (3, 1) (b) (2, 4) (c) (4, 2) (d) (8, 4)
  31. 31.What is the distance between the points (6, 5) and (18, 21)? (a) 28 (b) 20 (c) 400 (d) 21
  32. 32.What is the distance between the points (1, 8) and (13, 3)? (a) 169 (b) 13 (c) 17 (d) 14
  33. 33.How far is the point (12, 9) from the origin (0, 0)? (a) 21 (b) 225 (c) 16 (d) 15
  34. 34.What is the midpoint of the line joining (10, 3) and (12, 5)? (a) (4, 11) (b) (1, 1) (c) (11, 4) (d) (22, 8)
  35. 35.In which quadrant does the point (−9, −8) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  36. 36.What is the distance between the points (0, 17) and (12, 1)? (a) 400 (b) 21 (c) 28 (d) 20
  37. 37.What is the midpoint of the line joining (10, 6) and (16, 14)? (a) (26, 20) (b) (3, 4) (c) (10, 13) (d) (13, 10)
  38. 38.What is the distance between the points (0, 7) and (12, 16)? (a) 225 (b) 21 (c) 15 (d) 16
  39. 39.In which quadrant does the point (7, −2) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  40. 40.In which quadrant does the point (2, 8) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant

Answer key

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

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