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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 170 · 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 distance between the points (6, 3) and (10, 6)? (a) 5 (b) 6 (c) 7 (d) 25
  2. 2.How far is the point (12, 9) from the origin (0, 0)? (a) 225 (b) 16 (c) 15 (d) 21
  3. 3.What is the distance between the points (9, 2) and (14, 14)? (a) 17 (b) 14 (c) 169 (d) 13
  4. 4.What is the distance between the points (1, 8) and (9, 14)? (a) 100 (b) 11 (c) 10 (d) 14
  5. 5.What is the distance between the points (7, 5) and (15, 20)? (a) 289 (b) 23 (c) 18 (d) 17
  6. 6.What is the midpoint of the line joining (9, 9) and (15, 13)? (a) (3, 2) (b) (24, 22) (c) (12, 11) (d) (11, 12)
  7. 7.How far is the point (12, 16) from the origin (0, 0)? (a) 28 (b) 20 (c) 21 (d) 400
  8. 8.What is the distance between the points (9, 5) and (17, 20)? (a) 289 (b) 17 (c) 18 (d) 23
  9. 9.What is the midpoint of the line joining (5, 6) and (11, 8)? (a) (7, 8) (b) (3, 1) (c) (8, 7) (d) (16, 14)
  10. 10.In which quadrant does the point (6, 9) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  11. 11.In which quadrant does the point (6, 5) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  12. 12.What is the distance between the points (8, 9) and (14, 1)? (a) 14 (b) 100 (c) 10 (d) 11
  13. 13.In which quadrant does the point (−6, 4) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  14. 14.In which quadrant does the point (−5, 4) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  15. 15.What is the midpoint of the line joining (4, 14) and (14, 8)? (a) (9, 11) (b) (11, 9) (c) (5, 3) (d) (18, 22)
  16. 16.What is the distance between the points (6, 5) and (22, 17)? (a) 21 (b) 400 (c) 28 (d) 20
  17. 17.How far is the point (16, 12) from the origin (0, 0)? (a) 21 (b) 28 (c) 20 (d) 400
  18. 18.What is the midpoint of the line joining (9, 2) and (11, 14)? (a) (1, 6) (b) (8, 10) (c) (10, 8) (d) (20, 16)
  19. 19.How far is the point (6, 8) from the origin (0, 0)? (a) 11 (b) 10 (c) 100 (d) 14
  20. 20.How far is the point (7, 24) from the origin (0, 0)? (a) 31 (b) 25 (c) 625 (d) 26
  21. 21.What is the midpoint of the line joining (3, 13) and (15, 9)? (a) (9, 11) (b) (11, 9) (c) (18, 22) (d) (6, 2)
  22. 22.What is the midpoint of the line joining (1, 2) and (13, 8)? (a) (7, 5) (b) (14, 10) (c) (6, 3) (d) (5, 7)
  23. 23.What is the midpoint of the line joining (0, 9) and (10, 11)? (a) (10, 5) (b) (5, 1) (c) (5, 10) (d) (10, 20)
  24. 24.How far is the point (3, 4) from the origin (0, 0)? (a) 25 (b) 5 (c) 6 (d) 7
  25. 25.What is the midpoint of the line joining (7, 10) and (13, 22)? (a) (10, 16) (b) (16, 10) (c) (20, 32) (d) (3, 6)
  26. 26.What is the distance between the points (6, 8) and (14, 14)? (a) 100 (b) 10 (c) 11 (d) 14
  27. 27.In which quadrant does the point (−4, −6) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  28. 28.What is the distance between the points (8, 6) and (16, 0)? (a) 10 (b) 100 (c) 14 (d) 11
  29. 29.In which quadrant does the point (3, −8) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  30. 30.What is the midpoint of the line joining (7, 16) and (11, 8)? (a) (18, 24) (b) (9, 12) (c) (2, 4) (d) (12, 9)
  31. 31.What is the distance between the points (4, 18) and (12, 3)? (a) 23 (b) 17 (c) 289 (d) 18
  32. 32.In which quadrant does the point (−3, −6) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  33. 33.What is the midpoint of the line joining (7, 9) and (15, 11)? (a) (10, 11) (b) (22, 20) (c) (11, 10) (d) (4, 1)
  34. 34.What is the distance between the points (9, 18) and (21, 2)? (a) 28 (b) 400 (c) 21 (d) 20
  35. 35.What is the distance between the points (4, 20) and (13, 8)? (a) 21 (b) 225 (c) 16 (d) 15
  36. 36.What is the distance between the points (7, 21) and (15, 6)? (a) 17 (b) 289 (c) 18 (d) 23
  37. 37.In which quadrant does the point (−5, 5) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  38. 38.In which quadrant does the point (4, −4) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  39. 39.What is the midpoint of the line joining (6, 7) and (14, 17)? (a) (20, 24) (b) (4, 5) (c) (10, 12) (d) (12, 10)
  40. 40.In which quadrant does the point (−2, 9) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant

Answer key

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

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