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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 975 · 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 (4, 5) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  2. 2.In which quadrant does the point (−4, −3) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  3. 3.What is the midpoint of the line joining (4, 1) and (12, 11)? (a) (8, 6) (b) (4, 5) (c) (6, 8) (d) (16, 12)
  4. 4.What is the midpoint of the line joining (7, 21) and (11, 9)? (a) (2, 6) (b) (15, 9) (c) (9, 15) (d) (18, 30)
  5. 5.How far is the point (12, 5) from the origin (0, 0)? (a) 169 (b) 13 (c) 14 (d) 17
  6. 6.What is the distance between the points (2, 3) and (18, 15)? (a) 400 (b) 20 (c) 28 (d) 21
  7. 7.In which quadrant does the point (6, 6) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  8. 8.What is the distance between the points (7, 13) and (19, 8)? (a) 14 (b) 13 (c) 17 (d) 169
  9. 9.In which quadrant does the point (9, −3) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  10. 10.In which quadrant does the point (−4, 5) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  11. 11.What is the midpoint of the line joining (4, 10) and (16, 22)? (a) (16, 10) (b) (10, 16) (c) (6, 6) (d) (20, 32)
  12. 12.In which quadrant does the point (5, 1) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  13. 13.How far is the point (7, 24) from the origin (0, 0)? (a) 625 (b) 31 (c) 25 (d) 26
  14. 14.How far is the point (8, 15) from the origin (0, 0)? (a) 289 (b) 23 (c) 17 (d) 18
  15. 15.What is the distance between the points (0, 4) and (12, 20)? (a) 400 (b) 20 (c) 28 (d) 21
  16. 16.What is the midpoint of the line joining (0, 15) and (2, 7)? (a) (11, 1) (b) (2, 22) (c) (1, 4) (d) (1, 11)
  17. 17.In which quadrant does the point (2, 2) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  18. 18.What is the distance between the points (3, 10) and (27, 3)? (a) 25 (b) 26 (c) 625 (d) 31
  19. 19.In which quadrant does the point (−3, −6) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  20. 20.What is the midpoint of the line joining (0, 9) and (12, 1)? (a) (6, 4) (b) (12, 10) (c) (5, 6) (d) (6, 5)
  21. 21.What is the midpoint of the line joining (4, 2) and (6, 4)? (a) (5, 3) (b) (1, 1) (c) (3, 5) (d) (10, 6)
  22. 22.In which quadrant does the point (−2, −9) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  23. 23.In which quadrant does the point (−6, 1) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  24. 24.In which quadrant does the point (4, −3) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  25. 25.What is the midpoint of the line joining (0, 0) and (6, 4)? (a) (6, 4) (b) (3, 2) (c) (4, 2) (d) (2, 3)
  26. 26.How far is the point (16, 12) from the origin (0, 0)? (a) 28 (b) 21 (c) 20 (d) 400
  27. 27.What is the midpoint of the line joining (4, 9) and (12, 5)? (a) (16, 14) (b) (7, 8) (c) (8, 7) (d) (4, 2)
  28. 28.In which quadrant does the point (5, −4) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  29. 29.What is the midpoint of the line joining (5, 2) and (7, 6)? (a) (4, 6) (b) (6, 4) (c) (12, 8) (d) (1, 2)
  30. 30.How far is the point (5, 12) from the origin (0, 0)? (a) 17 (b) 13 (c) 169 (d) 14
  31. 31.What is the midpoint of the line joining (6, 13) and (12, 1)? (a) (9, 7) (b) (3, 6) (c) (7, 9) (d) (18, 14)
  32. 32.What is the midpoint of the line joining (2, 6) and (6, 8)? (a) (8, 14) (b) (7, 4) (c) (2, 1) (d) (4, 7)
  33. 33.In which quadrant does the point (6, 1) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  34. 34.What is the midpoint of the line joining (10, 2) and (22, 6)? (a) (32, 8) (b) (16, 4) (c) (4, 16) (d) (6, 2)
  35. 35.What is the midpoint of the line joining (9, 7) and (21, 3)? (a) (6, 2) (b) (5, 15) (c) (30, 10) (d) (15, 5)
  36. 36.In which quadrant does the point (4, −8) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  37. 37.How far is the point (24, 7) from the origin (0, 0)? (a) 25 (b) 31 (c) 625 (d) 26
  38. 38.What is the midpoint of the line joining (5, 8) and (9, 16)? (a) (12, 7) (b) (2, 4) (c) (14, 24) (d) (7, 12)
  39. 39.What is the midpoint of the line joining (2, 12) and (10, 4)? (a) (4, 4) (b) (8, 6) (c) (12, 16) (d) (6, 8)
  40. 40.What is the distance between the points (4, 8) and (7, 4)? (a) 25 (b) 5 (c) 6 (d) 7

Answer key

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

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