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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 177 · 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 (5, 3) and (17, 1)? (a) (11, 2) (b) (22, 4) (c) (6, 1) (d) (2, 11)
  2. 2.What is the distance between the points (3, 0) and (15, 16)? (a) 20 (b) 400 (c) 28 (d) 21
  3. 3.In which quadrant does the point (−5, −7) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  4. 4.What is the distance between the points (0, 18) and (9, 6)? (a) 15 (b) 225 (c) 21 (d) 16
  5. 5.How far is the point (12, 5) from the origin (0, 0)? (a) 17 (b) 169 (c) 13 (d) 14
  6. 6.What is the midpoint of the line joining (10, 6) and (22, 0)? (a) (6, 3) (b) (16, 3) (c) (32, 6) (d) (3, 16)
  7. 7.How far is the point (15, 8) from the origin (0, 0)? (a) 18 (b) 289 (c) 17 (d) 23
  8. 8.What is the distance between the points (2, 11) and (6, 8)? (a) 6 (b) 25 (c) 7 (d) 5
  9. 9.In which quadrant does the point (5, −2) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  10. 10.What is the distance between the points (5, 9) and (14, 21)? (a) 225 (b) 21 (c) 16 (d) 15
  11. 11.What is the distance between the points (3, 1) and (15, 6)? (a) 17 (b) 169 (c) 13 (d) 14
  12. 12.What is the distance between the points (1, 19) and (9, 4)? (a) 289 (b) 17 (c) 18 (d) 23
  13. 13.How far is the point (3, 4) from the origin (0, 0)? (a) 25 (b) 5 (c) 6 (d) 7
  14. 14.What is the distance between the points (7, 4) and (23, 16)? (a) 21 (b) 400 (c) 20 (d) 28
  15. 15.How far is the point (7, 24) from the origin (0, 0)? (a) 31 (b) 26 (c) 25 (d) 625
  16. 16.In which quadrant does the point (4, 1) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  17. 17.What is the midpoint of the line joining (5, 6) and (7, 4)? (a) (12, 10) (b) (6, 5) (c) (1, 1) (d) (5, 6)
  18. 18.How far is the point (8, 15) from the origin (0, 0)? (a) 23 (b) 17 (c) 289 (d) 18
  19. 19.How far is the point (9, 12) from the origin (0, 0)? (a) 15 (b) 21 (c) 16 (d) 225
  20. 20.What is the midpoint of the line joining (0, 1) and (8, 9)? (a) (8, 10) (b) (4, 4) (c) (4, 5) (d) (5, 4)
  21. 21.In which quadrant does the point (3, 2) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  22. 22.How far is the point (24, 7) from the origin (0, 0)? (a) 31 (b) 625 (c) 26 (d) 25
  23. 23.In which quadrant does the point (−6, 5) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  24. 24.What is the midpoint of the line joining (10, 2) and (16, 10)? (a) (3, 4) (b) (6, 13) (c) (26, 12) (d) (13, 6)
  25. 25.In which quadrant does the point (−8, −1) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  26. 26.What is the midpoint of the line joining (0, 9) and (2, 13)? (a) (1, 2) (b) (2, 22) (c) (11, 1) (d) (1, 11)
  27. 27.What is the midpoint of the line joining (9, 8) and (15, 18)? (a) (13, 12) (b) (3, 5) (c) (24, 26) (d) (12, 13)
  28. 28.In which quadrant does the point (1, 6) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  29. 29.In which quadrant does the point (−9, 2) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  30. 30.How far is the point (8, 6) from the origin (0, 0)? (a) 14 (b) 10 (c) 11 (d) 100
  31. 31.In which quadrant does the point (−6, −9) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  32. 32.In which quadrant does the point (−8, 9) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  33. 33.What is the midpoint of the line joining (2, 6) and (4, 12)? (a) (6, 18) (b) (9, 3) (c) (3, 9) (d) (1, 3)
  34. 34.In which quadrant does the point (1, −6) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  35. 35.What is the distance between the points (0, 4) and (5, 16)? (a) 14 (b) 13 (c) 169 (d) 17
  36. 36.What is the midpoint of the line joining (0, 7) and (4, 19)? (a) (2, 13) (b) (4, 26) (c) (13, 2) (d) (2, 6)
  37. 37.What is the midpoint of the line joining (2, 14) and (4, 2)? (a) (6, 16) (b) (3, 8) (c) (1, 6) (d) (8, 3)
  38. 38.How far is the point (16, 12) from the origin (0, 0)? (a) 28 (b) 21 (c) 20 (d) 400
  39. 39.What is the distance between the points (2, 30) and (9, 6)? (a) 625 (b) 31 (c) 26 (d) 25
  40. 40.How far is the point (6, 8) from the origin (0, 0)? (a) 14 (b) 100 (c) 11 (d) 10

Answer key

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

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