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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 69 · 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, 8) and (18, 24)? (a) 28 (b) 400 (c) 21 (d) 20
  2. 2.How far is the point (8, 6) from the origin (0, 0)? (a) 14 (b) 100 (c) 10 (d) 11
  3. 3.In which quadrant does the point (8, 1) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  4. 4.What is the midpoint of the line joining (0, 8) and (2, 6)? (a) (2, 14) (b) (7, 1) (c) (1, 7) (d) (1, 1)
  5. 5.In which quadrant does the point (−3, 1) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  6. 6.What is the distance between the points (5, 19) and (17, 3)? (a) 21 (b) 28 (c) 400 (d) 20
  7. 7.In which quadrant does the point (−3, −8) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  8. 8.What is the midpoint of the line joining (2, 10) and (12, 6)? (a) (14, 16) (b) (7, 8) (c) (8, 7) (d) (5, 2)
  9. 9.What is the midpoint of the line joining (7, 6) and (13, 2)? (a) (20, 8) (b) (3, 2) (c) (4, 10) (d) (10, 4)
  10. 10.What is the distance between the points (3, 3) and (11, 9)? (a) 100 (b) 11 (c) 10 (d) 14
  11. 11.How far is the point (16, 12) from the origin (0, 0)? (a) 21 (b) 28 (c) 400 (d) 20
  12. 12.In which quadrant does the point (−8, 4) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  13. 13.What is the distance between the points (1, 9) and (4, 5)? (a) 5 (b) 7 (c) 25 (d) 6
  14. 14.What is the distance between the points (8, 25) and (15, 1)? (a) 26 (b) 31 (c) 625 (d) 25
  15. 15.In which quadrant does the point (−7, −5) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  16. 16.What is the distance between the points (3, 12) and (27, 5)? (a) 25 (b) 625 (c) 31 (d) 26
  17. 17.What is the distance between the points (2, 17) and (14, 8)? (a) 15 (b) 21 (c) 16 (d) 225
  18. 18.In which quadrant does the point (−5, 1) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  19. 19.What is the distance between the points (5, 8) and (9, 5)? (a) 25 (b) 7 (c) 5 (d) 6
  20. 20.What is the distance between the points (9, 7) and (15, 15)? (a) 14 (b) 10 (c) 100 (d) 11
  21. 21.What is the distance between the points (2, 9) and (7, 21)? (a) 14 (b) 17 (c) 169 (d) 13
  22. 22.How far is the point (5, 12) from the origin (0, 0)? (a) 17 (b) 14 (c) 169 (d) 13
  23. 23.What is the distance between the points (1, 12) and (6, 0)? (a) 13 (b) 169 (c) 14 (d) 17
  24. 24.What is the distance between the points (4, 2) and (19, 10)? (a) 289 (b) 17 (c) 18 (d) 23
  25. 25.In which quadrant does the point (−6, 9) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  26. 26.What is the midpoint of the line joining (10, 15) and (12, 9)? (a) (1, 3) (b) (22, 24) (c) (11, 12) (d) (12, 11)
  27. 27.How far is the point (12, 16) from the origin (0, 0)? (a) 20 (b) 21 (c) 28 (d) 400
  28. 28.What is the distance between the points (0, 15) and (9, 3)? (a) 21 (b) 15 (c) 16 (d) 225
  29. 29.How far is the point (12, 5) from the origin (0, 0)? (a) 14 (b) 169 (c) 13 (d) 17
  30. 30.What is the distance between the points (3, 16) and (8, 4)? (a) 13 (b) 17 (c) 14 (d) 169
  31. 31.In which quadrant does the point (9, 3) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  32. 32.How far is the point (7, 24) from the origin (0, 0)? (a) 26 (b) 31 (c) 625 (d) 25
  33. 33.In which quadrant does the point (−4, 3) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  34. 34.How far is the point (9, 12) from the origin (0, 0)? (a) 21 (b) 225 (c) 16 (d) 15
  35. 35.How far is the point (8, 15) from the origin (0, 0)? (a) 289 (b) 23 (c) 18 (d) 17
  36. 36.What is the distance between the points (8, 24) and (15, 0)? (a) 31 (b) 625 (c) 25 (d) 26
  37. 37.What is the distance between the points (0, 0) and (24, 7)? (a) 31 (b) 625 (c) 26 (d) 25
  38. 38.In which quadrant does the point (7, −9) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  39. 39.What is the midpoint of the line joining (2, 3) and (8, 13)? (a) (10, 16) (b) (8, 5) (c) (5, 8) (d) (3, 5)
  40. 40.What is the distance between the points (1, 15) and (25, 8)? (a) 26 (b) 25 (c) 31 (d) 625

Answer key

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

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