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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 853 · 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 (4, 23) and (16, 7)? (a) 400 (b) 20 (c) 28 (d) 21
  2. 2.What is the midpoint of the line joining (1, 11) and (5, 3)? (a) (7, 3) (b) (6, 14) (c) (2, 4) (d) (3, 7)
  3. 3.What is the distance between the points (1, 9) and (13, 18)? (a) 225 (b) 16 (c) 15 (d) 21
  4. 4.What is the distance between the points (1, 10) and (4, 6)? (a) 6 (b) 5 (c) 25 (d) 7
  5. 5.What is the distance between the points (5, 10) and (13, 4)? (a) 100 (b) 10 (c) 11 (d) 14
  6. 6.What is the distance between the points (8, 15) and (14, 7)? (a) 10 (b) 11 (c) 100 (d) 14
  7. 7.In which quadrant does the point (−8, 9) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  8. 8.How far is the point (12, 9) from the origin (0, 0)? (a) 15 (b) 225 (c) 21 (d) 16
  9. 9.In which quadrant does the point (−3, −3) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  10. 10.What is the distance between the points (6, 2) and (14, 8)? (a) 11 (b) 10 (c) 100 (d) 14
  11. 11.In which quadrant does the point (8, 3) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  12. 12.What is the distance between the points (2, 22) and (10, 7)? (a) 18 (b) 23 (c) 17 (d) 289
  13. 13.What is the distance between the points (8, 8) and (16, 14)? (a) 14 (b) 11 (c) 10 (d) 100
  14. 14.What is the midpoint of the line joining (9, 13) and (21, 1)? (a) (7, 15) (b) (30, 14) (c) (6, 6) (d) (15, 7)
  15. 15.What is the midpoint of the line joining (2, 5) and (14, 3)? (a) (6, 1) (b) (16, 8) (c) (8, 4) (d) (4, 8)
  16. 16.What is the midpoint of the line joining (6, 3) and (8, 7)? (a) (1, 2) (b) (5, 7) (c) (7, 5) (d) (14, 10)
  17. 17.What is the midpoint of the line joining (7, 12) and (17, 0)? (a) (6, 12) (b) (5, 6) (c) (12, 6) (d) (24, 12)
  18. 18.How far is the point (12, 5) from the origin (0, 0)? (a) 169 (b) 13 (c) 17 (d) 14
  19. 19.How far is the point (15, 8) from the origin (0, 0)? (a) 17 (b) 18 (c) 289 (d) 23
  20. 20.In which quadrant does the point (5, 8) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  21. 21.How far is the point (3, 4) from the origin (0, 0)? (a) 5 (b) 7 (c) 25 (d) 6
  22. 22.What is the midpoint of the line joining (9, 5) and (15, 1)? (a) (24, 6) (b) (12, 3) (c) (3, 2) (d) (3, 12)
  23. 23.What is the distance between the points (2, 4) and (6, 1)? (a) 25 (b) 6 (c) 5 (d) 7
  24. 24.What is the distance between the points (8, 3) and (16, 9)? (a) 100 (b) 11 (c) 10 (d) 14
  25. 25.What is the midpoint of the line joining (8, 3) and (18, 11)? (a) (13, 7) (b) (26, 14) (c) (7, 13) (d) (5, 4)
  26. 26.What is the distance between the points (7, 6) and (31, 13)? (a) 625 (b) 26 (c) 31 (d) 25
  27. 27.What is the distance between the points (4, 4) and (7, 0)? (a) 25 (b) 7 (c) 6 (d) 5
  28. 28.What is the midpoint of the line joining (1, 13) and (13, 7)? (a) (7, 10) (b) (10, 7) (c) (6, 3) (d) (14, 20)
  29. 29.In which quadrant does the point (6, −5) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  30. 30.How far is the point (9, 12) from the origin (0, 0)? (a) 21 (b) 16 (c) 15 (d) 225
  31. 31.In which quadrant does the point (−8, 5) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  32. 32.In which quadrant does the point (9, 7) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  33. 33.What is the distance between the points (7, 7) and (13, 15)? (a) 100 (b) 14 (c) 10 (d) 11
  34. 34.What is the midpoint of the line joining (3, 9) and (13, 1)? (a) (8, 5) (b) (5, 4) (c) (16, 10) (d) (5, 8)
  35. 35.What is the distance between the points (4, 13) and (16, 8)? (a) 14 (b) 17 (c) 169 (d) 13
  36. 36.In which quadrant does the point (−5, 2) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  37. 37.What is the distance between the points (3, 6) and (11, 0)? (a) 100 (b) 14 (c) 11 (d) 10
  38. 38.How far is the point (6, 8) from the origin (0, 0)? (a) 10 (b) 14 (c) 11 (d) 100
  39. 39.How far is the point (24, 7) from the origin (0, 0)? (a) 25 (b) 625 (c) 26 (d) 31
  40. 40.In which quadrant does the point (1, −7) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant

Answer key

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

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