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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 822 · 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 (8, 1) and (16, 16)? (a) 17 (b) 289 (c) 18 (d) 23
  2. 2.What is the distance between the points (3, 5) and (10, 29)? (a) 31 (b) 625 (c) 25 (d) 26
  3. 3.What is the distance between the points (8, 2) and (24, 14)? (a) 21 (b) 20 (c) 400 (d) 28
  4. 4.How far is the point (8, 6) from the origin (0, 0)? (a) 100 (b) 10 (c) 14 (d) 11
  5. 5.In which quadrant does the point (1, 4) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  6. 6.In which quadrant does the point (−8, 9) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  7. 7.What is the midpoint of the line joining (5, 0) and (15, 12)? (a) (10, 6) (b) (6, 10) (c) (20, 12) (d) (5, 6)
  8. 8.In which quadrant does the point (9, 5) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  9. 9.In which quadrant does the point (6, 6) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  10. 10.What is the distance between the points (2, 13) and (11, 1)? (a) 16 (b) 15 (c) 225 (d) 21
  11. 11.What is the midpoint of the line joining (10, 16) and (12, 10)? (a) (13, 11) (b) (1, 3) (c) (22, 26) (d) (11, 13)
  12. 12.How far is the point (4, 3) from the origin (0, 0)? (a) 25 (b) 6 (c) 7 (d) 5
  13. 13.How far is the point (15, 8) from the origin (0, 0)? (a) 289 (b) 17 (c) 18 (d) 23
  14. 14.What is the distance between the points (3, 8) and (27, 1)? (a) 625 (b) 26 (c) 25 (d) 31
  15. 15.What is the midpoint of the line joining (1, 10) and (3, 22)? (a) (16, 2) (b) (1, 6) (c) (4, 32) (d) (2, 16)
  16. 16.What is the midpoint of the line joining (2, 12) and (4, 8)? (a) (10, 3) (b) (6, 20) (c) (1, 2) (d) (3, 10)
  17. 17.How far is the point (8, 15) from the origin (0, 0)? (a) 18 (b) 17 (c) 289 (d) 23
  18. 18.What is the midpoint of the line joining (5, 19) and (15, 9)? (a) (10, 14) (b) (14, 10) (c) (20, 28) (d) (5, 5)
  19. 19.In which quadrant does the point (1, 2) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  20. 20.What is the midpoint of the line joining (4, 8) and (8, 20)? (a) (14, 6) (b) (6, 14) (c) (12, 28) (d) (2, 6)
  21. 21.How far is the point (9, 12) from the origin (0, 0)? (a) 16 (b) 225 (c) 21 (d) 15
  22. 22.What is the distance between the points (4, 4) and (13, 16)? (a) 225 (b) 21 (c) 16 (d) 15
  23. 23.What is the distance between the points (6, 8) and (21, 0)? (a) 23 (b) 18 (c) 289 (d) 17
  24. 24.In which quadrant does the point (1, 1) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  25. 25.What is the distance between the points (1, 16) and (7, 8)? (a) 11 (b) 100 (c) 10 (d) 14
  26. 26.What is the midpoint of the line joining (8, 21) and (18, 9)? (a) (15, 13) (b) (26, 30) (c) (5, 6) (d) (13, 15)
  27. 27.In which quadrant does the point (9, 7) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  28. 28.In which quadrant does the point (−7, 2) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  29. 29.In which quadrant does the point (2, 6) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  30. 30.How far is the point (7, 24) from the origin (0, 0)? (a) 625 (b) 26 (c) 25 (d) 31
  31. 31.How far is the point (6, 8) from the origin (0, 0)? (a) 11 (b) 14 (c) 100 (d) 10
  32. 32.In which quadrant does the point (5, 6) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  33. 33.What is the midpoint of the line joining (9, 10) and (13, 8)? (a) (2, 1) (b) (9, 11) (c) (22, 18) (d) (11, 9)
  34. 34.What is the midpoint of the line joining (9, 0) and (17, 12)? (a) (26, 12) (b) (13, 6) (c) (4, 6) (d) (6, 13)
  35. 35.In which quadrant does the point (8, 3) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  36. 36.What is the distance between the points (3, 25) and (10, 1)? (a) 25 (b) 26 (c) 31 (d) 625
  37. 37.What is the distance between the points (7, 0) and (16, 12)? (a) 225 (b) 15 (c) 16 (d) 21
  38. 38.What is the midpoint of the line joining (6, 8) and (18, 6)? (a) (24, 14) (b) (12, 7) (c) (6, 1) (d) (7, 12)
  39. 39.What is the distance between the points (1, 18) and (6, 6)? (a) 169 (b) 17 (c) 13 (d) 14
  40. 40.What is the midpoint of the line joining (7, 14) and (9, 10)? (a) (8, 12) (b) (1, 2) (c) (12, 8) (d) (16, 24)

Answer key

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

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