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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 920 · 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 (2, −2) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  2. 2.In which quadrant does the point (−5, 8) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  3. 3.What is the midpoint of the line joining (3, 8) and (7, 20)? (a) (5, 14) (b) (14, 5) (c) (10, 28) (d) (2, 6)
  4. 4.How far is the point (24, 7) from the origin (0, 0)? (a) 26 (b) 25 (c) 625 (d) 31
  5. 5.What is the distance between the points (5, 26) and (12, 2)? (a) 31 (b) 26 (c) 25 (d) 625
  6. 6.What is the distance between the points (1, 33) and (8, 9)? (a) 625 (b) 26 (c) 25 (d) 31
  7. 7.How far is the point (9, 12) from the origin (0, 0)? (a) 16 (b) 21 (c) 15 (d) 225
  8. 8.How far is the point (4, 3) from the origin (0, 0)? (a) 6 (b) 25 (c) 7 (d) 5
  9. 9.What is the distance between the points (7, 16) and (22, 8)? (a) 289 (b) 18 (c) 17 (d) 23
  10. 10.What is the midpoint of the line joining (4, 18) and (14, 10)? (a) (14, 9) (b) (18, 28) (c) (5, 4) (d) (9, 14)
  11. 11.What is the distance between the points (1, 5) and (25, 12)? (a) 625 (b) 25 (c) 26 (d) 31
  12. 12.How far is the point (12, 5) from the origin (0, 0)? (a) 17 (b) 169 (c) 13 (d) 14
  13. 13.In which quadrant does the point (7, 1) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  14. 14.What is the midpoint of the line joining (1, 14) and (3, 8)? (a) (2, 11) (b) (4, 22) (c) (1, 3) (d) (11, 2)
  15. 15.What is the distance between the points (8, 12) and (13, 0)? (a) 169 (b) 17 (c) 14 (d) 13
  16. 16.How far is the point (15, 8) from the origin (0, 0)? (a) 18 (b) 17 (c) 23 (d) 289
  17. 17.What is the distance between the points (7, 5) and (22, 13)? (a) 18 (b) 23 (c) 17 (d) 289
  18. 18.What is the distance between the points (0, 1) and (8, 7)? (a) 14 (b) 11 (c) 10 (d) 100
  19. 19.In which quadrant does the point (7, 8) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  20. 20.What is the distance between the points (9, 3) and (12, 7)? (a) 6 (b) 5 (c) 25 (d) 7
  21. 21.What is the distance between the points (3, 0) and (7, 3)? (a) 7 (b) 25 (c) 5 (d) 6
  22. 22.What is the distance between the points (7, 4) and (13, 12)? (a) 14 (b) 100 (c) 10 (d) 11
  23. 23.What is the midpoint of the line joining (7, 4) and (19, 6)? (a) (6, 1) (b) (5, 13) (c) (13, 5) (d) (26, 10)
  24. 24.What is the midpoint of the line joining (0, 19) and (10, 9)? (a) (5, 14) (b) (5, 5) (c) (14, 5) (d) (10, 28)
  25. 25.In which quadrant does the point (4, 2) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  26. 26.What is the midpoint of the line joining (6, 10) and (8, 16)? (a) (1, 3) (b) (14, 26) (c) (7, 13) (d) (13, 7)
  27. 27.What is the midpoint of the line joining (9, 0) and (11, 6)? (a) (1, 3) (b) (3, 10) (c) (20, 6) (d) (10, 3)
  28. 28.What is the midpoint of the line joining (3, 17) and (15, 9)? (a) (9, 13) (b) (6, 4) (c) (13, 9) (d) (18, 26)
  29. 29.What is the distance between the points (5, 2) and (17, 7)? (a) 169 (b) 13 (c) 14 (d) 17
  30. 30.In which quadrant does the point (−5, −2) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  31. 31.In which quadrant does the point (−3, 2) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  32. 32.How far is the point (5, 12) from the origin (0, 0)? (a) 169 (b) 14 (c) 17 (d) 13
  33. 33.What is the distance between the points (0, 8) and (4, 5)? (a) 5 (b) 25 (c) 6 (d) 7
  34. 34.What is the distance between the points (8, 3) and (20, 12)? (a) 21 (b) 15 (c) 225 (d) 16
  35. 35.What is the midpoint of the line joining (7, 0) and (11, 6)? (a) (18, 6) (b) (3, 9) (c) (2, 3) (d) (9, 3)
  36. 36.What is the distance between the points (2, 15) and (14, 6)? (a) 15 (b) 16 (c) 21 (d) 225
  37. 37.What is the distance between the points (5, 4) and (17, 13)? (a) 21 (b) 225 (c) 16 (d) 15
  38. 38.What is the midpoint of the line joining (7, 1) and (13, 9)? (a) (20, 10) (b) (10, 5) (c) (5, 10) (d) (3, 4)
  39. 39.What is the distance between the points (0, 5) and (8, 11)? (a) 11 (b) 14 (c) 10 (d) 100
  40. 40.In which quadrant does the point (1, −4) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant

Answer key

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

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