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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 122 · 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 (−3, −8) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  2. 2.In which quadrant does the point (−5, −6) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  3. 3.What is the distance between the points (3, 12) and (8, 0)? (a) 13 (b) 169 (c) 17 (d) 14
  4. 4.What is the distance between the points (1, 14) and (13, 5)? (a) 225 (b) 21 (c) 16 (d) 15
  5. 5.What is the midpoint of the line joining (7, 4) and (15, 2)? (a) (11, 3) (b) (22, 6) (c) (4, 1) (d) (3, 11)
  6. 6.How far is the point (8, 6) from the origin (0, 0)? (a) 11 (b) 10 (c) 100 (d) 14
  7. 7.How far is the point (12, 16) from the origin (0, 0)? (a) 28 (b) 21 (c) 20 (d) 400
  8. 8.In which quadrant does the point (5, 9) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  9. 9.What is the distance between the points (1, 3) and (4, 7)? (a) 5 (b) 25 (c) 7 (d) 6
  10. 10.What is the midpoint of the line joining (9, 10) and (17, 6)? (a) (8, 13) (b) (4, 2) (c) (13, 8) (d) (26, 16)
  11. 11.What is the midpoint of the line joining (10, 9) and (16, 7)? (a) (8, 13) (b) (3, 1) (c) (26, 16) (d) (13, 8)
  12. 12.How far is the point (15, 8) from the origin (0, 0)? (a) 17 (b) 289 (c) 18 (d) 23
  13. 13.How far is the point (3, 4) from the origin (0, 0)? (a) 6 (b) 5 (c) 25 (d) 7
  14. 14.What is the distance between the points (0, 13) and (5, 1)? (a) 13 (b) 14 (c) 17 (d) 169
  15. 15.In which quadrant does the point (4, 3) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  16. 16.In which quadrant does the point (8, 4) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  17. 17.In which quadrant does the point (4, −3) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  18. 18.In which quadrant does the point (2, 5) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  19. 19.What is the distance between the points (6, 17) and (15, 5)? (a) 21 (b) 225 (c) 16 (d) 15
  20. 20.What is the midpoint of the line joining (4, 10) and (14, 6)? (a) (9, 8) (b) (8, 9) (c) (5, 2) (d) (18, 16)
  21. 21.What is the distance between the points (3, 13) and (12, 1)? (a) 21 (b) 16 (c) 225 (d) 15
  22. 22.What is the distance between the points (4, 2) and (28, 9)? (a) 25 (b) 625 (c) 26 (d) 31
  23. 23.How far is the point (4, 3) from the origin (0, 0)? (a) 7 (b) 5 (c) 6 (d) 25
  24. 24.What is the distance between the points (1, 4) and (4, 8)? (a) 6 (b) 7 (c) 25 (d) 5
  25. 25.What is the distance between the points (1, 3) and (6, 15)? (a) 17 (b) 169 (c) 14 (d) 13
  26. 26.What is the distance between the points (8, 1) and (13, 13)? (a) 13 (b) 169 (c) 14 (d) 17
  27. 27.What is the midpoint of the line joining (9, 9) and (17, 5)? (a) (26, 14) (b) (7, 13) (c) (4, 2) (d) (13, 7)
  28. 28.What is the midpoint of the line joining (8, 8) and (10, 20)? (a) (1, 6) (b) (18, 28) (c) (14, 9) (d) (9, 14)
  29. 29.What is the distance between the points (4, 9) and (12, 15)? (a) 11 (b) 10 (c) 100 (d) 14
  30. 30.What is the distance between the points (6, 0) and (14, 6)? (a) 14 (b) 100 (c) 10 (d) 11
  31. 31.What is the midpoint of the line joining (5, 3) and (15, 5)? (a) (4, 10) (b) (20, 8) (c) (5, 1) (d) (10, 4)
  32. 32.In which quadrant does the point (−4, 8) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  33. 33.How far is the point (9, 12) from the origin (0, 0)? (a) 16 (b) 21 (c) 225 (d) 15
  34. 34.What is the midpoint of the line joining (3, 12) and (7, 2)? (a) (5, 7) (b) (10, 14) (c) (2, 5) (d) (7, 5)
  35. 35.In which quadrant does the point (−5, −1) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  36. 36.What is the distance between the points (0, 20) and (12, 4)? (a) 400 (b) 21 (c) 28 (d) 20
  37. 37.What is the midpoint of the line joining (0, 13) and (6, 7)? (a) (6, 20) (b) (10, 3) (c) (3, 10) (d) (3, 3)
  38. 38.In which quadrant does the point (2, 3) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  39. 39.In which quadrant does the point (6, 5) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  40. 40.How far is the point (12, 5) from the origin (0, 0)? (a) 13 (b) 17 (c) 14 (d) 169

Answer key

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

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