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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 162 · 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 (2, 4) and (10, 19)? (a) 18 (b) 289 (c) 17 (d) 23
  2. 2.In which quadrant does the point (8, 6) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  3. 3.What is the midpoint of the line joining (5, 12) and (13, 2)? (a) (18, 14) (b) (9, 7) (c) (7, 9) (d) (4, 5)
  4. 4.What is the distance between the points (0, 11) and (4, 8)? (a) 6 (b) 5 (c) 25 (d) 7
  5. 5.What is the midpoint of the line joining (6, 7) and (16, 17)? (a) (11, 12) (b) (12, 11) (c) (22, 24) (d) (5, 5)
  6. 6.What is the distance between the points (8, 11) and (12, 8)? (a) 25 (b) 6 (c) 5 (d) 7
  7. 7.How far is the point (24, 7) from the origin (0, 0)? (a) 26 (b) 31 (c) 625 (d) 25
  8. 8.What is the distance between the points (0, 7) and (24, 0)? (a) 26 (b) 31 (c) 25 (d) 625
  9. 9.In which quadrant does the point (6, −4) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  10. 10.What is the midpoint of the line joining (9, 10) and (21, 18)? (a) (14, 15) (b) (30, 28) (c) (15, 14) (d) (6, 4)
  11. 11.What is the midpoint of the line joining (7, 19) and (11, 7)? (a) (18, 26) (b) (13, 9) (c) (2, 6) (d) (9, 13)
  12. 12.How far is the point (5, 12) from the origin (0, 0)? (a) 14 (b) 169 (c) 13 (d) 17
  13. 13.What is the midpoint of the line joining (9, 11) and (11, 7)? (a) (20, 18) (b) (10, 9) (c) (1, 2) (d) (9, 10)
  14. 14.What is the distance between the points (7, 6) and (12, 18)? (a) 169 (b) 14 (c) 13 (d) 17
  15. 15.In which quadrant does the point (−3, −4) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  16. 16.In which quadrant does the point (1, 2) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  17. 17.How far is the point (7, 24) from the origin (0, 0)? (a) 26 (b) 25 (c) 31 (d) 625
  18. 18.How far is the point (12, 5) from the origin (0, 0)? (a) 14 (b) 17 (c) 13 (d) 169
  19. 19.What is the distance between the points (9, 33) and (16, 9)? (a) 25 (b) 26 (c) 31 (d) 625
  20. 20.What is the distance between the points (4, 0) and (7, 4)? (a) 5 (b) 25 (c) 6 (d) 7
  21. 21.What is the midpoint of the line joining (4, 1) and (8, 5)? (a) (2, 2) (b) (6, 3) (c) (3, 6) (d) (12, 6)
  22. 22.In which quadrant does the point (2, −6) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  23. 23.In which quadrant does the point (−2, 7) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  24. 24.How far is the point (3, 4) from the origin (0, 0)? (a) 25 (b) 7 (c) 5 (d) 6
  25. 25.What is the midpoint of the line joining (8, 10) and (18, 4)? (a) (5, 3) (b) (26, 14) (c) (13, 7) (d) (7, 13)
  26. 26.What is the distance between the points (3, 6) and (18, 14)? (a) 17 (b) 18 (c) 23 (d) 289
  27. 27.What is the distance between the points (0, 6) and (12, 1)? (a) 14 (b) 13 (c) 169 (d) 17
  28. 28.What is the distance between the points (0, 8) and (24, 15)? (a) 25 (b) 625 (c) 31 (d) 26
  29. 29.What is the midpoint of the line joining (4, 14) and (16, 6)? (a) (6, 4) (b) (20, 20) (c) (11, 10) (d) (10, 10)
  30. 30.What is the midpoint of the line joining (5, 2) and (7, 10)? (a) (7, 6) (b) (6, 6) (c) (12, 12) (d) (1, 4)
  31. 31.What is the midpoint of the line joining (3, 14) and (7, 6)? (a) (10, 5) (b) (5, 10) (c) (2, 4) (d) (10, 20)
  32. 32.How far is the point (12, 9) from the origin (0, 0)? (a) 15 (b) 16 (c) 225 (d) 21
  33. 33.In which quadrant does the point (−8, 1) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  34. 34.What is the distance between the points (4, 1) and (13, 13)? (a) 21 (b) 15 (c) 16 (d) 225
  35. 35.What is the distance between the points (5, 3) and (13, 18)? (a) 17 (b) 23 (c) 18 (d) 289
  36. 36.What is the distance between the points (9, 8) and (15, 0)? (a) 10 (b) 11 (c) 14 (d) 100
  37. 37.How far is the point (8, 15) from the origin (0, 0)? (a) 17 (b) 23 (c) 289 (d) 18
  38. 38.What is the midpoint of the line joining (10, 10) and (12, 12)? (a) (12, 11) (b) (11, 11) (c) (22, 22) (d) (1, 1)
  39. 39.What is the midpoint of the line joining (5, 7) and (9, 17)? (a) (12, 7) (b) (14, 24) (c) (7, 12) (d) (2, 5)
  40. 40.How far is the point (6, 8) from the origin (0, 0)? (a) 11 (b) 14 (c) 100 (d) 10

Answer key

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

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