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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 681 · 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 (0, 8) and (12, 14)? (a) (12, 22) (b) (11, 6) (c) (6, 11) (d) (6, 3)
  2. 2.In which quadrant does the point (−3, −8) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  3. 3.How far is the point (4, 3) from the origin (0, 0)? (a) 6 (b) 25 (c) 5 (d) 7
  4. 4.How far is the point (12, 16) from the origin (0, 0)? (a) 21 (b) 20 (c) 28 (d) 400
  5. 5.What is the midpoint of the line joining (9, 4) and (21, 16)? (a) (6, 6) (b) (30, 20) (c) (15, 10) (d) (10, 15)
  6. 6.How far is the point (6, 8) from the origin (0, 0)? (a) 100 (b) 10 (c) 11 (d) 14
  7. 7.In which quadrant does the point (−5, 1) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  8. 8.What is the midpoint of the line joining (3, 13) and (7, 7)? (a) (10, 5) (b) (5, 10) (c) (10, 20) (d) (2, 3)
  9. 9.In which quadrant does the point (−6, 6) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  10. 10.What is the distance between the points (6, 8) and (18, 17)? (a) 16 (b) 21 (c) 225 (d) 15
  11. 11.What is the distance between the points (8, 10) and (16, 4)? (a) 14 (b) 100 (c) 10 (d) 11
  12. 12.What is the midpoint of the line joining (8, 9) and (18, 11)? (a) (5, 1) (b) (10, 13) (c) (26, 20) (d) (13, 10)
  13. 13.What is the distance between the points (9, 3) and (13, 0)? (a) 6 (b) 25 (c) 7 (d) 5
  14. 14.What is the distance between the points (7, 11) and (15, 5)? (a) 11 (b) 100 (c) 14 (d) 10
  15. 15.What is the distance between the points (9, 0) and (12, 4)? (a) 5 (b) 25 (c) 7 (d) 6
  16. 16.How far is the point (8, 15) from the origin (0, 0)? (a) 17 (b) 23 (c) 289 (d) 18
  17. 17.What is the distance between the points (6, 15) and (18, 6)? (a) 16 (b) 15 (c) 21 (d) 225
  18. 18.What is the distance between the points (9, 2) and (17, 17)? (a) 23 (b) 18 (c) 289 (d) 17
  19. 19.What is the midpoint of the line joining (7, 15) and (15, 5)? (a) (4, 5) (b) (11, 10) (c) (10, 11) (d) (22, 20)
  20. 20.How far is the point (3, 4) from the origin (0, 0)? (a) 7 (b) 5 (c) 25 (d) 6
  21. 21.What is the distance between the points (4, 9) and (12, 3)? (a) 100 (b) 14 (c) 11 (d) 10
  22. 22.What is the midpoint of the line joining (5, 1) and (15, 9)? (a) (5, 10) (b) (5, 4) (c) (10, 5) (d) (20, 10)
  23. 23.In which quadrant does the point (1, 7) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  24. 24.What is the midpoint of the line joining (9, 1) and (15, 9)? (a) (5, 12) (b) (3, 4) (c) (12, 5) (d) (24, 10)
  25. 25.In which quadrant does the point (6, 6) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  26. 26.What is the midpoint of the line joining (0, 1) and (8, 7)? (a) (4, 4) (b) (5, 4) (c) (8, 8) (d) (4, 3)
  27. 27.What is the distance between the points (8, 33) and (15, 9)? (a) 26 (b) 625 (c) 31 (d) 25
  28. 28.What is the distance between the points (7, 16) and (15, 1)? (a) 289 (b) 23 (c) 18 (d) 17
  29. 29.What is the distance between the points (8, 0) and (20, 16)? (a) 20 (b) 21 (c) 28 (d) 400
  30. 30.What is the midpoint of the line joining (1, 12) and (9, 8)? (a) (4, 2) (b) (10, 20) (c) (10, 5) (d) (5, 10)
  31. 31.What is the midpoint of the line joining (4, 9) and (12, 7)? (a) (4, 1) (b) (9, 8) (c) (8, 8) (d) (16, 16)
  32. 32.In which quadrant does the point (8, −6) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
  33. 33.What is the midpoint of the line joining (2, 3) and (6, 13)? (a) (8, 16) (b) (8, 4) (c) (2, 5) (d) (4, 8)
  34. 34.How far is the point (8, 6) from the origin (0, 0)? (a) 100 (b) 10 (c) 14 (d) 11
  35. 35.In which quadrant does the point (−1, −3) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  36. 36.What is the distance between the points (0, 2) and (7, 26)? (a) 25 (b) 26 (c) 625 (d) 31
  37. 37.What is the distance between the points (1, 0) and (9, 6)? (a) 14 (b) 100 (c) 11 (d) 10
  38. 38.What is the distance between the points (5, 7) and (21, 19)? (a) 28 (b) 21 (c) 20 (d) 400
  39. 39.What is the midpoint of the line joining (2, 7) and (6, 19)? (a) (13, 4) (b) (2, 6) (c) (8, 26) (d) (4, 13)
  40. 40.What is the distance between the points (5, 12) and (29, 5)? (a) 31 (b) 26 (c) 25 (d) 625

Answer key

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

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