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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 548 · 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 (8, 8) and (10, 12)? (a) (1, 2) (b) (9, 10) (c) (18, 20) (d) (10, 9)
  2. 2.What is the midpoint of the line joining (10, 7) and (20, 15)? (a) (30, 22) (b) (5, 4) (c) (11, 15) (d) (15, 11)
  3. 3.What is the midpoint of the line joining (10, 19) and (22, 7)? (a) (6, 6) (b) (16, 13) (c) (32, 26) (d) (13, 16)
  4. 4.How far is the point (12, 16) from the origin (0, 0)? (a) 20 (b) 28 (c) 400 (d) 21
  5. 5.What is the distance between the points (0, 2) and (6, 10)? (a) 11 (b) 14 (c) 10 (d) 100
  6. 6.What is the midpoint of the line joining (4, 8) and (12, 6)? (a) (16, 14) (b) (4, 1) (c) (8, 7) (d) (7, 8)
  7. 7.How far is the point (12, 5) from the origin (0, 0)? (a) 13 (b) 14 (c) 17 (d) 169
  8. 8.What is the distance between the points (5, 9) and (12, 33)? (a) 25 (b) 26 (c) 31 (d) 625
  9. 9.In which quadrant does the point (−7, −6) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  10. 10.How far is the point (3, 4) from the origin (0, 0)? (a) 25 (b) 6 (c) 7 (d) 5
  11. 11.What is the distance between the points (4, 9) and (12, 24)? (a) 17 (b) 18 (c) 289 (d) 23
  12. 12.What is the midpoint of the line joining (0, 5) and (6, 11)? (a) (6, 16) (b) (3, 3) (c) (3, 8) (d) (8, 3)
  13. 13.What is the distance between the points (7, 2) and (22, 10)? (a) 18 (b) 23 (c) 289 (d) 17
  14. 14.What is the midpoint of the line joining (3, 10) and (7, 2)? (a) (5, 6) (b) (2, 4) (c) (6, 5) (d) (10, 12)
  15. 15.What is the midpoint of the line joining (4, 15) and (16, 5)? (a) (11, 10) (b) (10, 10) (c) (20, 20) (d) (6, 5)
  16. 16.What is the midpoint of the line joining (3, 20) and (13, 8)? (a) (16, 28) (b) (8, 14) (c) (5, 6) (d) (14, 8)
  17. 17.What is the distance between the points (6, 5) and (15, 17)? (a) 16 (b) 21 (c) 225 (d) 15
  18. 18.What is the distance between the points (7, 2) and (12, 14)? (a) 17 (b) 169 (c) 14 (d) 13
  19. 19.How far is the point (24, 7) from the origin (0, 0)? (a) 625 (b) 26 (c) 31 (d) 25
  20. 20.In which quadrant does the point (3, 8) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  21. 21.How far is the point (9, 12) from the origin (0, 0)? (a) 225 (b) 16 (c) 15 (d) 21
  22. 22.What is the midpoint of the line joining (1, 15) and (7, 3)? (a) (9, 4) (b) (8, 18) (c) (3, 6) (d) (4, 9)
  23. 23.In which quadrant does the point (−8, −8) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  24. 24.What is the distance between the points (1, 7) and (10, 19)? (a) 15 (b) 21 (c) 225 (d) 16
  25. 25.In which quadrant does the point (−2, −4) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  26. 26.What is the distance between the points (8, 1) and (15, 25)? (a) 625 (b) 25 (c) 31 (d) 26
  27. 27.What is the distance between the points (5, 9) and (8, 13)? (a) 6 (b) 5 (c) 25 (d) 7
  28. 28.What is the distance between the points (7, 8) and (13, 16)? (a) 11 (b) 100 (c) 14 (d) 10
  29. 29.What is the distance between the points (6, 9) and (11, 21)? (a) 14 (b) 17 (c) 169 (d) 13
  30. 30.What is the distance between the points (4, 3) and (20, 15)? (a) 20 (b) 400 (c) 28 (d) 21
  31. 31.What is the midpoint of the line joining (3, 6) and (5, 18)? (a) (1, 6) (b) (4, 12) (c) (8, 24) (d) (12, 4)
  32. 32.In which quadrant does the point (−9, −4) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  33. 33.What is the midpoint of the line joining (5, 9) and (11, 19)? (a) (16, 28) (b) (3, 5) (c) (14, 8) (d) (8, 14)
  34. 34.How far is the point (4, 3) from the origin (0, 0)? (a) 25 (b) 5 (c) 7 (d) 6
  35. 35.In which quadrant does the point (−8, 9) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  36. 36.What is the midpoint of the line joining (2, 3) and (6, 13)? (a) (4, 8) (b) (8, 4) (c) (8, 16) (d) (2, 5)
  37. 37.How far is the point (16, 12) from the origin (0, 0)? (a) 21 (b) 20 (c) 28 (d) 400
  38. 38.In which quadrant does the point (−5, −8) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  39. 39.How far is the point (5, 12) from the origin (0, 0)? (a) 17 (b) 14 (c) 13 (d) 169
  40. 40.What is the distance between the points (9, 4) and (12, 8)? (a) 7 (b) 5 (c) 25 (d) 6

Answer key

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

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