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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 47 · 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.How far is the point (4, 3) from the origin (0, 0)? (a) 25 (b) 5 (c) 6 (d) 7
  2. 2.What is the midpoint of the line joining (0, 10) and (4, 12)? (a) (11, 2) (b) (2, 11) (c) (4, 22) (d) (2, 1)
  3. 3.How far is the point (5, 12) from the origin (0, 0)? (a) 14 (b) 17 (c) 13 (d) 169
  4. 4.How far is the point (8, 6) from the origin (0, 0)? (a) 100 (b) 10 (c) 11 (d) 14
  5. 5.What is the midpoint of the line joining (9, 3) and (17, 9)? (a) (26, 12) (b) (13, 6) (c) (4, 3) (d) (6, 13)
  6. 6.What is the midpoint of the line joining (3, 13) and (15, 7)? (a) (10, 9) (b) (18, 20) (c) (9, 10) (d) (6, 3)
  7. 7.What is the midpoint of the line joining (3, 4) and (15, 2)? (a) (3, 9) (b) (9, 3) (c) (18, 6) (d) (6, 1)
  8. 8.How far is the point (3, 4) from the origin (0, 0)? (a) 5 (b) 6 (c) 25 (d) 7
  9. 9.What is the distance between the points (1, 1) and (13, 17)? (a) 20 (b) 400 (c) 21 (d) 28
  10. 10.What is the distance between the points (4, 6) and (16, 1)? (a) 14 (b) 13 (c) 17 (d) 169
  11. 11.In which quadrant does the point (2, 8) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  12. 12.What is the midpoint of the line joining (9, 12) and (19, 8)? (a) (5, 2) (b) (28, 20) (c) (10, 14) (d) (14, 10)
  13. 13.How far is the point (8, 15) from the origin (0, 0)? (a) 289 (b) 17 (c) 18 (d) 23
  14. 14.What is the midpoint of the line joining (7, 10) and (19, 18)? (a) (6, 4) (b) (13, 14) (c) (26, 28) (d) (14, 13)
  15. 15.What is the distance between the points (0, 8) and (8, 2)? (a) 11 (b) 10 (c) 14 (d) 100
  16. 16.What is the distance between the points (2, 11) and (10, 5)? (a) 14 (b) 100 (c) 11 (d) 10
  17. 17.What is the distance between the points (9, 6) and (17, 0)? (a) 11 (b) 100 (c) 14 (d) 10
  18. 18.What is the midpoint of the line joining (1, 8) and (9, 20)? (a) (14, 5) (b) (4, 6) (c) (5, 14) (d) (10, 28)
  19. 19.What is the distance between the points (2, 4) and (10, 19)? (a) 23 (b) 18 (c) 289 (d) 17
  20. 20.What is the distance between the points (0, 21) and (12, 5)? (a) 400 (b) 21 (c) 20 (d) 28
  21. 21.What is the midpoint of the line joining (9, 6) and (17, 2)? (a) (13, 4) (b) (26, 8) (c) (4, 2) (d) (4, 13)
  22. 22.What is the distance between the points (5, 11) and (11, 3)? (a) 11 (b) 14 (c) 10 (d) 100
  23. 23.How far is the point (12, 5) from the origin (0, 0)? (a) 17 (b) 169 (c) 14 (d) 13
  24. 24.In which quadrant does the point (−4, −2) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  25. 25.How far is the point (9, 12) from the origin (0, 0)? (a) 15 (b) 21 (c) 225 (d) 16
  26. 26.In which quadrant does the point (1, 4) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  27. 27.What is the distance between the points (7, 12) and (16, 0)? (a) 16 (b) 15 (c) 225 (d) 21
  28. 28.In which quadrant does the point (3, 1) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  29. 29.What is the distance between the points (2, 9) and (17, 17)? (a) 18 (b) 23 (c) 17 (d) 289
  30. 30.How far is the point (15, 8) from the origin (0, 0)? (a) 23 (b) 18 (c) 17 (d) 289
  31. 31.In which quadrant does the point (4, 7) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  32. 32.In which quadrant does the point (9, 6) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  33. 33.What is the midpoint of the line joining (0, 10) and (2, 0)? (a) (2, 5) (b) (2, 10) (c) (5, 1) (d) (1, 5)
  34. 34.How far is the point (16, 12) from the origin (0, 0)? (a) 20 (b) 28 (c) 21 (d) 400
  35. 35.What is the distance between the points (1, 0) and (13, 16)? (a) 28 (b) 21 (c) 400 (d) 20
  36. 36.What is the distance between the points (4, 13) and (16, 8)? (a) 169 (b) 14 (c) 17 (d) 13
  37. 37.What is the distance between the points (1, 8) and (6, 20)? (a) 17 (b) 14 (c) 169 (d) 13
  38. 38.What is the midpoint of the line joining (7, 2) and (15, 0)? (a) (1, 11) (b) (22, 2) (c) (11, 1) (d) (4, 1)
  39. 39.How far is the point (7, 24) from the origin (0, 0)? (a) 26 (b) 25 (c) 625 (d) 31
  40. 40.What is the midpoint of the line joining (8, 14) and (12, 2)? (a) (10, 8) (b) (20, 16) (c) (8, 10) (d) (2, 6)

Answer key

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

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