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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 396 · 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 (24, 7) from the origin (0, 0)? (a) 31 (b) 25 (c) 26 (d) 625
  2. 2.How far is the point (3, 4) from the origin (0, 0)? (a) 5 (b) 25 (c) 6 (d) 7
  3. 3.What is the midpoint of the line joining (3, 8) and (11, 20)? (a) (4, 6) (b) (14, 7) (c) (14, 28) (d) (7, 14)
  4. 4.What is the midpoint of the line joining (8, 0) and (10, 4)? (a) (18, 4) (b) (1, 2) (c) (9, 2) (d) (2, 9)
  5. 5.What is the distance between the points (9, 20) and (18, 8)? (a) 16 (b) 15 (c) 225 (d) 21
  6. 6.What is the midpoint of the line joining (7, 3) and (17, 9)? (a) (12, 6) (b) (5, 3) (c) (6, 12) (d) (24, 12)
  7. 7.In which quadrant does the point (−1, 9) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  8. 8.In which quadrant does the point (3, 1) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  9. 9.What is the midpoint of the line joining (10, 3) and (22, 7)? (a) (5, 16) (b) (32, 10) (c) (16, 5) (d) (6, 2)
  10. 10.In which quadrant does the point (7, 4) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
  11. 11.How far is the point (15, 8) from the origin (0, 0)? (a) 17 (b) 18 (c) 23 (d) 289
  12. 12.In which quadrant does the point (−9, 7) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  13. 13.In which quadrant does the point (−4, −3) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  14. 14.What is the midpoint of the line joining (3, 16) and (5, 10)? (a) (4, 13) (b) (1, 3) (c) (8, 26) (d) (13, 4)
  15. 15.What is the midpoint of the line joining (2, 10) and (8, 12)? (a) (11, 5) (b) (5, 11) (c) (10, 22) (d) (3, 1)
  16. 16.How far is the point (8, 15) from the origin (0, 0)? (a) 18 (b) 17 (c) 289 (d) 23
  17. 17.What is the distance between the points (1, 3) and (16, 11)? (a) 23 (b) 18 (c) 17 (d) 289
  18. 18.How far is the point (8, 6) from the origin (0, 0)? (a) 11 (b) 10 (c) 14 (d) 100
  19. 19.In which quadrant does the point (7, 7) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  20. 20.What is the distance between the points (4, 3) and (16, 12)? (a) 21 (b) 225 (c) 15 (d) 16
  21. 21.What is the distance between the points (0, 7) and (16, 19)? (a) 400 (b) 28 (c) 20 (d) 21
  22. 22.What is the distance between the points (9, 1) and (25, 13)? (a) 21 (b) 28 (c) 400 (d) 20
  23. 23.What is the distance between the points (6, 1) and (18, 17)? (a) 21 (b) 20 (c) 28 (d) 400
  24. 24.What is the distance between the points (8, 1) and (17, 13)? (a) 15 (b) 21 (c) 225 (d) 16
  25. 25.What is the distance between the points (0, 7) and (8, 13)? (a) 14 (b) 10 (c) 11 (d) 100
  26. 26.What is the distance between the points (7, 7) and (19, 23)? (a) 21 (b) 400 (c) 20 (d) 28
  27. 27.What is the distance between the points (9, 0) and (16, 24)? (a) 625 (b) 26 (c) 25 (d) 31
  28. 28.What is the distance between the points (1, 4) and (6, 16)? (a) 17 (b) 169 (c) 14 (d) 13
  29. 29.What is the distance between the points (7, 6) and (15, 0)? (a) 100 (b) 11 (c) 10 (d) 14
  30. 30.How far is the point (12, 5) from the origin (0, 0)? (a) 169 (b) 17 (c) 14 (d) 13
  31. 31.What is the midpoint of the line joining (9, 5) and (21, 15)? (a) (10, 15) (b) (30, 20) (c) (15, 10) (d) (6, 5)
  32. 32.What is the distance between the points (7, 8) and (15, 23)? (a) 289 (b) 23 (c) 18 (d) 17
  33. 33.How far is the point (9, 12) from the origin (0, 0)? (a) 15 (b) 225 (c) 21 (d) 16
  34. 34.In which quadrant does the point (8, −3) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  35. 35.What is the midpoint of the line joining (7, 5) and (17, 13)? (a) (5, 4) (b) (24, 18) (c) (12, 9) (d) (9, 12)
  36. 36.What is the distance between the points (0, 0) and (5, 12)? (a) 14 (b) 169 (c) 17 (d) 13
  37. 37.What is the distance between the points (7, 24) and (14, 0)? (a) 26 (b) 625 (c) 25 (d) 31
  38. 38.In which quadrant does the point (−1, −3) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  39. 39.How far is the point (12, 9) from the origin (0, 0)? (a) 16 (b) 225 (c) 15 (d) 21
  40. 40.What is the distance between the points (6, 4) and (30, 11)? (a) 31 (b) 26 (c) 625 (d) 25

Answer key

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

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