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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 73 · 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, 4) and (12, 12)? (a) 14 (b) 100 (c) 11 (d) 10
  2. 2.How far is the point (3, 4) from the origin (0, 0)? (a) 7 (b) 25 (c) 5 (d) 6
  3. 3.What is the midpoint of the line joining (6, 10) and (12, 12)? (a) (9, 11) (b) (3, 1) (c) (18, 22) (d) (11, 9)
  4. 4.What is the midpoint of the line joining (4, 4) and (16, 6)? (a) (20, 10) (b) (5, 10) (c) (6, 1) (d) (10, 5)
  5. 5.In which quadrant does the point (9, 3) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  6. 6.What is the distance between the points (4, 19) and (9, 7)? (a) 14 (b) 169 (c) 13 (d) 17
  7. 7.In which quadrant does the point (−9, 5) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  8. 8.What is the midpoint of the line joining (0, 11) and (2, 7)? (a) (9, 1) (b) (1, 9) (c) (2, 18) (d) (1, 2)
  9. 9.What is the midpoint of the line joining (0, 5) and (12, 9)? (a) (12, 14) (b) (7, 6) (c) (6, 2) (d) (6, 7)
  10. 10.In which quadrant does the point (3, 2) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  11. 11.What is the midpoint of the line joining (2, 14) and (10, 8)? (a) (11, 6) (b) (4, 3) (c) (6, 11) (d) (12, 22)
  12. 12.How far is the point (6, 8) from the origin (0, 0)? (a) 11 (b) 14 (c) 10 (d) 100
  13. 13.What is the midpoint of the line joining (1, 3) and (7, 7)? (a) (3, 2) (b) (4, 5) (c) (8, 10) (d) (5, 4)
  14. 14.In which quadrant does the point (4, 6) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  15. 15.What is the distance between the points (5, 9) and (14, 21)? (a) 21 (b) 225 (c) 15 (d) 16
  16. 16.In which quadrant does the point (9, 6) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  17. 17.How far is the point (15, 8) from the origin (0, 0)? (a) 18 (b) 289 (c) 17 (d) 23
  18. 18.What is the distance between the points (1, 21) and (6, 9)? (a) 14 (b) 169 (c) 13 (d) 17
  19. 19.What is the distance between the points (3, 8) and (19, 20)? (a) 21 (b) 400 (c) 20 (d) 28
  20. 20.How far is the point (16, 12) from the origin (0, 0)? (a) 400 (b) 20 (c) 21 (d) 28
  21. 21.What is the distance between the points (2, 7) and (10, 13)? (a) 14 (b) 100 (c) 10 (d) 11
  22. 22.In which quadrant does the point (−7, −9) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  23. 23.What is the midpoint of the line joining (1, 4) and (11, 16)? (a) (12, 20) (b) (6, 10) (c) (5, 6) (d) (10, 6)
  24. 24.What is the midpoint of the line joining (9, 10) and (15, 2)? (a) (3, 4) (b) (24, 12) (c) (12, 6) (d) (6, 12)
  25. 25.In which quadrant does the point (−7, 9) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  26. 26.What is the midpoint of the line joining (2, 6) and (14, 14)? (a) (8, 10) (b) (6, 4) (c) (16, 20) (d) (10, 8)
  27. 27.What is the distance between the points (7, 18) and (12, 6)? (a) 13 (b) 169 (c) 14 (d) 17
  28. 28.What is the distance between the points (8, 2) and (20, 18)? (a) 28 (b) 20 (c) 21 (d) 400
  29. 29.In which quadrant does the point (−6, −6) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  30. 30.How far is the point (7, 24) from the origin (0, 0)? (a) 31 (b) 25 (c) 625 (d) 26
  31. 31.How far is the point (12, 9) from the origin (0, 0)? (a) 16 (b) 21 (c) 15 (d) 225
  32. 32.In which quadrant does the point (−8, −3) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  33. 33.What is the midpoint of the line joining (0, 9) and (12, 3)? (a) (12, 12) (b) (6, 6) (c) (6, 3) (d) (7, 6)
  34. 34.In which quadrant does the point (−3, −2) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  35. 35.What is the distance between the points (6, 16) and (21, 8)? (a) 18 (b) 289 (c) 17 (d) 23
  36. 36.What is the distance between the points (5, 10) and (13, 4)? (a) 14 (b) 100 (c) 11 (d) 10
  37. 37.What is the distance between the points (7, 16) and (16, 4)? (a) 225 (b) 16 (c) 15 (d) 21
  38. 38.In which quadrant does the point (−3, 7) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  39. 39.What is the midpoint of the line joining (8, 8) and (16, 20)? (a) (12, 14) (b) (4, 6) (c) (24, 28) (d) (14, 12)
  40. 40.What is the distance between the points (3, 6) and (6, 2)? (a) 6 (b) 25 (c) 7 (d) 5

Answer key

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

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