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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 949 · 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 (6, 13) and (8, 5)? (a) (9, 7) (b) (1, 4) (c) (14, 18) (d) (7, 9)
  2. 2.What is the midpoint of the line joining (6, 2) and (18, 14)? (a) (24, 16) (b) (6, 6) (c) (12, 8) (d) (8, 12)
  3. 3.What is the distance between the points (1, 17) and (13, 8)? (a) 21 (b) 16 (c) 225 (d) 15
  4. 4.How far is the point (9, 12) from the origin (0, 0)? (a) 21 (b) 15 (c) 16 (d) 225
  5. 5.What is the distance between the points (4, 0) and (7, 4)? (a) 7 (b) 25 (c) 6 (d) 5
  6. 6.What is the distance between the points (3, 9) and (8, 21)? (a) 14 (b) 13 (c) 169 (d) 17
  7. 7.What is the midpoint of the line joining (5, 0) and (13, 10)? (a) (4, 5) (b) (5, 9) (c) (9, 5) (d) (18, 10)
  8. 8.In which quadrant does the point (−6, −2) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  9. 9.How far is the point (12, 16) from the origin (0, 0)? (a) 400 (b) 20 (c) 28 (d) 21
  10. 10.What is the midpoint of the line joining (1, 18) and (5, 10)? (a) (3, 14) (b) (2, 4) (c) (14, 3) (d) (6, 28)
  11. 11.What is the midpoint of the line joining (0, 0) and (2, 12)? (a) (2, 12) (b) (1, 6) (c) (2, 6) (d) (6, 1)
  12. 12.What is the midpoint of the line joining (0, 5) and (2, 7)? (a) (6, 1) (b) (1, 6) (c) (2, 12) (d) (1, 1)
  13. 13.How far is the point (8, 15) from the origin (0, 0)? (a) 23 (b) 17 (c) 289 (d) 18
  14. 14.What is the distance between the points (1, 8) and (17, 20)? (a) 21 (b) 400 (c) 20 (d) 28
  15. 15.What is the distance between the points (8, 32) and (15, 8)? (a) 625 (b) 31 (c) 26 (d) 25
  16. 16.What is the midpoint of the line joining (8, 2) and (14, 6)? (a) (3, 2) (b) (22, 8) (c) (11, 4) (d) (4, 11)
  17. 17.What is the midpoint of the line joining (0, 11) and (6, 5)? (a) (3, 8) (b) (8, 3) (c) (3, 3) (d) (6, 16)
  18. 18.How far is the point (7, 24) from the origin (0, 0)? (a) 625 (b) 25 (c) 31 (d) 26
  19. 19.How far is the point (4, 3) from the origin (0, 0)? (a) 5 (b) 6 (c) 7 (d) 25
  20. 20.In which quadrant does the point (5, −1) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  21. 21.What is the distance between the points (1, 12) and (17, 0)? (a) 20 (b) 21 (c) 400 (d) 28
  22. 22.What is the distance between the points (2, 2) and (18, 14)? (a) 21 (b) 28 (c) 20 (d) 400
  23. 23.In which quadrant does the point (7, 9) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  24. 24.What is the distance between the points (1, 0) and (9, 15)? (a) 23 (b) 18 (c) 289 (d) 17
  25. 25.In which quadrant does the point (4, −5) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  26. 26.In which quadrant does the point (9, 8) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  27. 27.In which quadrant does the point (−2, −1) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  28. 28.What is the distance between the points (8, 8) and (16, 14)? (a) 100 (b) 14 (c) 10 (d) 11
  29. 29.In which quadrant does the point (2, 3) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
  30. 30.In which quadrant does the point (4, −7) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  31. 31.What is the distance between the points (3, 12) and (19, 0)? (a) 28 (b) 20 (c) 400 (d) 21
  32. 32.In which quadrant does the point (7, −9) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  33. 33.In which quadrant does the point (1, −2) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  34. 34.What is the midpoint of the line joining (2, 0) and (10, 2)? (a) (1, 6) (b) (4, 1) (c) (6, 1) (d) (12, 2)
  35. 35.What is the distance between the points (5, 15) and (10, 3)? (a) 169 (b) 17 (c) 13 (d) 14
  36. 36.How far is the point (8, 6) from the origin (0, 0)? (a) 10 (b) 100 (c) 14 (d) 11
  37. 37.What is the midpoint of the line joining (7, 9) and (19, 15)? (a) (26, 24) (b) (12, 13) (c) (6, 3) (d) (13, 12)
  38. 38.What is the distance between the points (0, 2) and (8, 17)? (a) 23 (b) 17 (c) 18 (d) 289
  39. 39.How far is the point (15, 8) from the origin (0, 0)? (a) 17 (b) 23 (c) 18 (d) 289
  40. 40.What is the distance between the points (0, 6) and (4, 9)? (a) 25 (b) 6 (c) 5 (d) 7

Answer key

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

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