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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 490 · 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.In which quadrant does the point (−7, −7) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  2. 2.What is the distance between the points (4, 10) and (12, 4)? (a) 100 (b) 10 (c) 11 (d) 14
  3. 3.How far is the point (8, 6) from the origin (0, 0)? (a) 14 (b) 10 (c) 11 (d) 100
  4. 4.What is the distance between the points (1, 9) and (13, 25)? (a) 28 (b) 400 (c) 20 (d) 21
  5. 5.How far is the point (9, 12) from the origin (0, 0)? (a) 16 (b) 15 (c) 225 (d) 21
  6. 6.In which quadrant does the point (−9, 3) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  7. 7.How far is the point (12, 16) from the origin (0, 0)? (a) 20 (b) 21 (c) 400 (d) 28
  8. 8.How far is the point (6, 8) from the origin (0, 0)? (a) 10 (b) 11 (c) 14 (d) 100
  9. 9.In which quadrant does the point (4, 6) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  10. 10.What is the midpoint of the line joining (0, 10) and (6, 2)? (a) (6, 12) (b) (3, 6) (c) (3, 4) (d) (6, 3)
  11. 11.What is the distance between the points (4, 2) and (16, 18)? (a) 28 (b) 400 (c) 21 (d) 20
  12. 12.How far is the point (4, 3) from the origin (0, 0)? (a) 7 (b) 5 (c) 6 (d) 25
  13. 13.How far is the point (15, 8) from the origin (0, 0)? (a) 289 (b) 18 (c) 17 (d) 23
  14. 14.What is the distance between the points (6, 4) and (14, 19)? (a) 18 (b) 17 (c) 23 (d) 289
  15. 15.In which quadrant does the point (7, −1) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  16. 16.In which quadrant does the point (−1, −8) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  17. 17.What is the midpoint of the line joining (10, 14) and (22, 6)? (a) (32, 20) (b) (6, 4) (c) (10, 16) (d) (16, 10)
  18. 18.What is the midpoint of the line joining (2, 19) and (10, 7)? (a) (13, 6) (b) (4, 6) (c) (12, 26) (d) (6, 13)
  19. 19.What is the distance between the points (6, 5) and (15, 17)? (a) 21 (b) 16 (c) 225 (d) 15
  20. 20.What is the distance between the points (1, 9) and (9, 24)? (a) 23 (b) 18 (c) 17 (d) 289
  21. 21.How far is the point (7, 24) from the origin (0, 0)? (a) 31 (b) 25 (c) 26 (d) 625
  22. 22.What is the midpoint of the line joining (4, 10) and (10, 2)? (a) (7, 6) (b) (6, 7) (c) (14, 12) (d) (3, 4)
  23. 23.What is the distance between the points (8, 6) and (13, 18)? (a) 17 (b) 14 (c) 13 (d) 169
  24. 24.How far is the point (24, 7) from the origin (0, 0)? (a) 26 (b) 31 (c) 625 (d) 25
  25. 25.What is the distance between the points (2, 3) and (7, 15)? (a) 14 (b) 17 (c) 169 (d) 13
  26. 26.What is the distance between the points (8, 5) and (12, 8)? (a) 7 (b) 5 (c) 25 (d) 6
  27. 27.In which quadrant does the point (−5, 8) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  28. 28.What is the distance between the points (0, 5) and (7, 29)? (a) 26 (b) 31 (c) 25 (d) 625
  29. 29.How far is the point (3, 4) from the origin (0, 0)? (a) 6 (b) 5 (c) 7 (d) 25
  30. 30.What is the midpoint of the line joining (7, 6) and (17, 18)? (a) (12, 12) (b) (13, 12) (c) (24, 24) (d) (5, 6)
  31. 31.What is the distance between the points (6, 2) and (22, 14)? (a) 28 (b) 21 (c) 400 (d) 20
  32. 32.How far is the point (12, 5) from the origin (0, 0)? (a) 17 (b) 14 (c) 13 (d) 169
  33. 33.In which quadrant does the point (−3, 2) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  34. 34.What is the distance between the points (3, 13) and (18, 5)? (a) 289 (b) 18 (c) 17 (d) 23
  35. 35.What is the midpoint of the line joining (3, 2) and (9, 8)? (a) (6, 5) (b) (3, 3) (c) (12, 10) (d) (5, 6)
  36. 36.What is the distance between the points (8, 3) and (20, 19)? (a) 20 (b) 400 (c) 21 (d) 28
  37. 37.What is the midpoint of the line joining (3, 6) and (15, 16)? (a) (18, 22) (b) (6, 5) (c) (11, 9) (d) (9, 11)
  38. 38.What is the distance between the points (6, 0) and (9, 4)? (a) 7 (b) 6 (c) 5 (d) 25
  39. 39.What is the distance between the points (1, 21) and (9, 6)? (a) 289 (b) 17 (c) 23 (d) 18
  40. 40.What is the distance between the points (2, 5) and (6, 2)? (a) 25 (b) 7 (c) 6 (d) 5

Answer key

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

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