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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 82 · 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 (8, 6) and (11, 10)? (a) 5 (b) 25 (c) 7 (d) 6
  2. 2.What is the midpoint of the line joining (2, 1) and (6, 9)? (a) (2, 4) (b) (5, 4) (c) (8, 10) (d) (4, 5)
  3. 3.What is the distance between the points (1, 13) and (7, 5)? (a) 14 (b) 100 (c) 11 (d) 10
  4. 4.What is the distance between the points (2, 6) and (6, 3)? (a) 7 (b) 6 (c) 25 (d) 5
  5. 5.In which quadrant does the point (5, −6) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  6. 6.What is the midpoint of the line joining (0, 10) and (8, 20)? (a) (15, 4) (b) (8, 30) (c) (4, 15) (d) (4, 5)
  7. 7.What is the distance between the points (0, 17) and (9, 5)? (a) 21 (b) 16 (c) 225 (d) 15
  8. 8.How far is the point (5, 12) from the origin (0, 0)? (a) 17 (b) 14 (c) 13 (d) 169
  9. 9.How far is the point (4, 3) from the origin (0, 0)? (a) 25 (b) 5 (c) 6 (d) 7
  10. 10.What is the distance between the points (4, 6) and (7, 10)? (a) 25 (b) 7 (c) 5 (d) 6
  11. 11.What is the distance between the points (7, 23) and (19, 7)? (a) 20 (b) 21 (c) 400 (d) 28
  12. 12.What is the midpoint of the line joining (9, 3) and (15, 7)? (a) (3, 2) (b) (12, 5) (c) (24, 10) (d) (5, 12)
  13. 13.How far is the point (16, 12) from the origin (0, 0)? (a) 21 (b) 400 (c) 20 (d) 28
  14. 14.What is the distance between the points (4, 14) and (10, 6)? (a) 10 (b) 14 (c) 100 (d) 11
  15. 15.How far is the point (12, 9) from the origin (0, 0)? (a) 16 (b) 15 (c) 225 (d) 21
  16. 16.What is the distance between the points (5, 5) and (17, 0)? (a) 13 (b) 17 (c) 169 (d) 14
  17. 17.In which quadrant does the point (−5, 6) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  18. 18.In which quadrant does the point (−8, −3) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  19. 19.What is the distance between the points (9, 11) and (15, 3)? (a) 11 (b) 100 (c) 10 (d) 14
  20. 20.What is the midpoint of the line joining (9, 1) and (17, 9)? (a) (4, 4) (b) (26, 10) (c) (5, 13) (d) (13, 5)
  21. 21.How far is the point (9, 12) from the origin (0, 0)? (a) 15 (b) 225 (c) 21 (d) 16
  22. 22.How far is the point (12, 16) from the origin (0, 0)? (a) 28 (b) 20 (c) 21 (d) 400
  23. 23.What is the midpoint of the line joining (4, 10) and (6, 14)? (a) (12, 5) (b) (5, 12) (c) (1, 2) (d) (10, 24)
  24. 24.What is the midpoint of the line joining (2, 4) and (14, 10)? (a) (7, 8) (b) (6, 3) (c) (16, 14) (d) (8, 7)
  25. 25.What is the distance between the points (0, 7) and (3, 3)? (a) 25 (b) 7 (c) 6 (d) 5
  26. 26.What is the distance between the points (8, 19) and (24, 7)? (a) 28 (b) 20 (c) 21 (d) 400
  27. 27.What is the distance between the points (4, 17) and (16, 8)? (a) 16 (b) 21 (c) 15 (d) 225
  28. 28.How far is the point (8, 6) from the origin (0, 0)? (a) 14 (b) 11 (c) 10 (d) 100
  29. 29.In which quadrant does the point (1, 9) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  30. 30.In which quadrant does the point (−6, −3) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  31. 31.What is the distance between the points (5, 2) and (20, 10)? (a) 17 (b) 23 (c) 18 (d) 289
  32. 32.What is the distance between the points (4, 5) and (11, 29)? (a) 625 (b) 31 (c) 25 (d) 26
  33. 33.What is the distance between the points (8, 25) and (15, 1)? (a) 625 (b) 31 (c) 25 (d) 26
  34. 34.What is the midpoint of the line joining (0, 3) and (8, 13)? (a) (8, 16) (b) (4, 5) (c) (4, 8) (d) (8, 4)
  35. 35.What is the midpoint of the line joining (3, 8) and (5, 20)? (a) (8, 28) (b) (14, 4) (c) (1, 6) (d) (4, 14)
  36. 36.In which quadrant does the point (−7, 9) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  37. 37.In which quadrant does the point (1, −6) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  38. 38.How far is the point (24, 7) from the origin (0, 0)? (a) 25 (b) 31 (c) 625 (d) 26
  39. 39.What is the midpoint of the line joining (9, 14) and (11, 2)? (a) (20, 16) (b) (1, 6) (c) (8, 10) (d) (10, 8)
  40. 40.What is the midpoint of the line joining (9, 14) and (21, 6)? (a) (15, 10) (b) (6, 4) (c) (30, 20) (d) (10, 15)

Answer key

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

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