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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 56 · 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 midpoint of the line joining (10, 16) and (14, 4)? (a) (2, 6) (b) (24, 20) (c) (12, 10) (d) (10, 12)
  2. 2.In which quadrant does the point (1, 1) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  3. 3.What is the midpoint of the line joining (1, 14) and (9, 2)? (a) (5, 8) (b) (4, 6) (c) (10, 16) (d) (8, 5)
  4. 4.What is the distance between the points (3, 14) and (18, 6)? (a) 23 (b) 17 (c) 18 (d) 289
  5. 5.In which quadrant does the point (6, 8) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  6. 6.What is the distance between the points (5, 8) and (29, 15)? (a) 26 (b) 625 (c) 31 (d) 25
  7. 7.What is the distance between the points (6, 17) and (15, 5)? (a) 21 (b) 16 (c) 225 (d) 15
  8. 8.In which quadrant does the point (−7, −9) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  9. 9.What is the midpoint of the line joining (8, 15) and (16, 5)? (a) (4, 5) (b) (10, 12) (c) (24, 20) (d) (12, 10)
  10. 10.How far is the point (6, 8) from the origin (0, 0)? (a) 14 (b) 11 (c) 10 (d) 100
  11. 11.How far is the point (4, 3) from the origin (0, 0)? (a) 7 (b) 6 (c) 25 (d) 5
  12. 12.What is the midpoint of the line joining (2, 14) and (6, 8)? (a) (4, 11) (b) (2, 3) (c) (8, 22) (d) (11, 4)
  13. 13.In which quadrant does the point (1, 5) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  14. 14.What is the midpoint of the line joining (0, 18) and (6, 8)? (a) (3, 5) (b) (6, 26) (c) (13, 3) (d) (3, 13)
  15. 15.How far is the point (8, 15) from the origin (0, 0)? (a) 17 (b) 289 (c) 18 (d) 23
  16. 16.What is the distance between the points (2, 4) and (18, 16)? (a) 20 (b) 28 (c) 400 (d) 21
  17. 17.What is the distance between the points (0, 14) and (15, 6)? (a) 23 (b) 17 (c) 289 (d) 18
  18. 18.What is the midpoint of the line joining (1, 2) and (9, 6)? (a) (10, 8) (b) (5, 4) (c) (4, 2) (d) (4, 5)
  19. 19.How far is the point (12, 16) from the origin (0, 0)? (a) 400 (b) 28 (c) 21 (d) 20
  20. 20.In which quadrant does the point (1, −7) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
  21. 21.What is the midpoint of the line joining (1, 16) and (9, 4)? (a) (10, 5) (b) (4, 6) (c) (10, 20) (d) (5, 10)
  22. 22.In which quadrant does the point (−9, 1) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  23. 23.What is the midpoint of the line joining (9, 11) and (15, 3)? (a) (12, 7) (b) (7, 12) (c) (3, 4) (d) (24, 14)
  24. 24.In which quadrant does the point (9, 9) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  25. 25.What is the distance between the points (8, 16) and (16, 1)? (a) 18 (b) 289 (c) 17 (d) 23
  26. 26.What is the distance between the points (3, 10) and (18, 2)? (a) 289 (b) 23 (c) 18 (d) 17
  27. 27.What is the midpoint of the line joining (1, 0) and (11, 4)? (a) (5, 2) (b) (12, 4) (c) (6, 2) (d) (2, 6)
  28. 28.What is the midpoint of the line joining (2, 8) and (4, 16)? (a) (3, 12) (b) (6, 24) (c) (1, 4) (d) (12, 3)
  29. 29.What is the distance between the points (4, 8) and (19, 16)? (a) 23 (b) 289 (c) 17 (d) 18
  30. 30.What is the distance between the points (4, 1) and (13, 13)? (a) 21 (b) 16 (c) 225 (d) 15
  31. 31.In which quadrant does the point (−2, −6) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  32. 32.How far is the point (3, 4) from the origin (0, 0)? (a) 25 (b) 5 (c) 6 (d) 7
  33. 33.How far is the point (15, 8) from the origin (0, 0)? (a) 18 (b) 23 (c) 289 (d) 17
  34. 34.In which quadrant does the point (8, 5) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  35. 35.What is the distance between the points (2, 2) and (10, 17)? (a) 23 (b) 289 (c) 18 (d) 17
  36. 36.What is the distance between the points (6, 8) and (14, 2)? (a) 100 (b) 14 (c) 10 (d) 11
  37. 37.What is the midpoint of the line joining (5, 5) and (17, 17)? (a) (6, 6) (b) (22, 22) (c) (12, 11) (d) (11, 11)
  38. 38.What is the distance between the points (9, 4) and (12, 0)? (a) 6 (b) 25 (c) 5 (d) 7
  39. 39.What is the distance between the points (1, 0) and (4, 4)? (a) 6 (b) 25 (c) 5 (d) 7
  40. 40.How far is the point (24, 7) from the origin (0, 0)? (a) 25 (b) 31 (c) 26 (d) 625

Answer key

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

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