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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 280 · 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, 6) and (19, 14)? (a) 289 (b) 18 (c) 17 (d) 23
  2. 2.In which quadrant does the point (−4, 8) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  3. 3.What is the midpoint of the line joining (5, 3) and (17, 5)? (a) (6, 1) (b) (22, 8) (c) (11, 4) (d) (4, 11)
  4. 4.What is the midpoint of the line joining (5, 2) and (17, 0)? (a) (22, 2) (b) (11, 1) (c) (6, 1) (d) (1, 11)
  5. 5.What is the midpoint of the line joining (6, 4) and (12, 6)? (a) (9, 5) (b) (18, 10) (c) (5, 9) (d) (3, 1)
  6. 6.What is the midpoint of the line joining (4, 8) and (14, 20)? (a) (9, 14) (b) (14, 9) (c) (18, 28) (d) (5, 6)
  7. 7.How far is the point (24, 7) from the origin (0, 0)? (a) 31 (b) 25 (c) 625 (d) 26
  8. 8.What is the midpoint of the line joining (1, 16) and (5, 8)? (a) (3, 12) (b) (2, 4) (c) (6, 24) (d) (12, 3)
  9. 9.What is the midpoint of the line joining (2, 8) and (6, 2)? (a) (2, 3) (b) (5, 4) (c) (8, 10) (d) (4, 5)
  10. 10.What is the distance between the points (7, 14) and (23, 2)? (a) 28 (b) 400 (c) 20 (d) 21
  11. 11.In which quadrant does the point (−4, −2) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  12. 12.How far is the point (5, 12) from the origin (0, 0)? (a) 14 (b) 13 (c) 169 (d) 17
  13. 13.What is the midpoint of the line joining (0, 9) and (10, 15)? (a) (10, 24) (b) (5, 3) (c) (12, 5) (d) (5, 12)
  14. 14.What is the midpoint of the line joining (8, 7) and (18, 15)? (a) (5, 4) (b) (26, 22) (c) (11, 13) (d) (13, 11)
  15. 15.How far is the point (15, 8) from the origin (0, 0)? (a) 289 (b) 17 (c) 23 (d) 18
  16. 16.What is the distance between the points (9, 3) and (21, 19)? (a) 28 (b) 400 (c) 21 (d) 20
  17. 17.What is the distance between the points (5, 1) and (17, 10)? (a) 225 (b) 15 (c) 21 (d) 16
  18. 18.What is the distance between the points (5, 7) and (9, 4)? (a) 25 (b) 7 (c) 5 (d) 6
  19. 19.What is the distance between the points (9, 21) and (17, 6)? (a) 23 (b) 18 (c) 17 (d) 289
  20. 20.What is the midpoint of the line joining (2, 22) and (6, 10)? (a) (8, 32) (b) (2, 6) (c) (16, 4) (d) (4, 16)
  21. 21.What is the midpoint of the line joining (0, 1) and (4, 5)? (a) (4, 6) (b) (3, 2) (c) (2, 2) (d) (2, 3)
  22. 22.What is the midpoint of the line joining (5, 5) and (17, 11)? (a) (8, 11) (b) (22, 16) (c) (6, 3) (d) (11, 8)
  23. 23.What is the distance between the points (7, 15) and (15, 9)? (a) 10 (b) 14 (c) 11 (d) 100
  24. 24.How far is the point (12, 5) from the origin (0, 0)? (a) 17 (b) 13 (c) 14 (d) 169
  25. 25.In which quadrant does the point (3, 2) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  26. 26.In which quadrant does the point (−3, 9) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  27. 27.What is the midpoint of the line joining (9, 1) and (21, 11)? (a) (6, 15) (b) (15, 6) (c) (6, 5) (d) (30, 12)
  28. 28.In which quadrant does the point (−9, 9) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  29. 29.How far is the point (6, 8) from the origin (0, 0)? (a) 14 (b) 10 (c) 100 (d) 11
  30. 30.In which quadrant does the point (8, 4) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  31. 31.What is the distance between the points (6, 7) and (10, 10)? (a) 7 (b) 6 (c) 5 (d) 25
  32. 32.What is the distance between the points (2, 2) and (6, 5)? (a) 6 (b) 7 (c) 5 (d) 25
  33. 33.In which quadrant does the point (4, −7) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  34. 34.In which quadrant does the point (9, 7) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  35. 35.How far is the point (8, 15) from the origin (0, 0)? (a) 289 (b) 23 (c) 18 (d) 17
  36. 36.What is the midpoint of the line joining (4, 3) and (8, 15)? (a) (9, 6) (b) (2, 6) (c) (6, 9) (d) (12, 18)
  37. 37.What is the midpoint of the line joining (0, 9) and (4, 17)? (a) (13, 2) (b) (2, 13) (c) (4, 26) (d) (2, 4)
  38. 38.How far is the point (3, 4) from the origin (0, 0)? (a) 7 (b) 25 (c) 5 (d) 6
  39. 39.How far is the point (12, 9) from the origin (0, 0)? (a) 21 (b) 16 (c) 225 (d) 15
  40. 40.What is the midpoint of the line joining (7, 1) and (17, 11)? (a) (6, 12) (b) (12, 6) (c) (5, 5) (d) (24, 12)

Answer key

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

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