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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 441 · 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 (9, 12) from the origin (0, 0)? (a) 21 (b) 225 (c) 16 (d) 15
  2. 2.In which quadrant does the point (9, 3) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  3. 3.What is the midpoint of the line joining (1, 12) and (9, 0)? (a) (4, 6) (b) (5, 6) (c) (6, 5) (d) (10, 12)
  4. 4.What is the midpoint of the line joining (3, 8) and (13, 0)? (a) (5, 4) (b) (8, 4) (c) (16, 8) (d) (4, 8)
  5. 5.How far is the point (8, 6) from the origin (0, 0)? (a) 100 (b) 10 (c) 14 (d) 11
  6. 6.What is the midpoint of the line joining (0, 10) and (4, 16)? (a) (4, 26) (b) (2, 3) (c) (13, 2) (d) (2, 13)
  7. 7.What is the distance between the points (7, 11) and (22, 3)? (a) 289 (b) 23 (c) 18 (d) 17
  8. 8.How far is the point (7, 24) from the origin (0, 0)? (a) 625 (b) 31 (c) 25 (d) 26
  9. 9.What is the distance between the points (2, 8) and (11, 20)? (a) 21 (b) 15 (c) 225 (d) 16
  10. 10.What is the midpoint of the line joining (7, 10) and (13, 18)? (a) (20, 28) (b) (14, 10) (c) (3, 4) (d) (10, 14)
  11. 11.What is the midpoint of the line joining (7, 4) and (15, 2)? (a) (4, 1) (b) (22, 6) (c) (11, 3) (d) (3, 11)
  12. 12.What is the midpoint of the line joining (8, 12) and (20, 8)? (a) (6, 2) (b) (28, 20) (c) (14, 10) (d) (10, 14)
  13. 13.How far is the point (4, 3) from the origin (0, 0)? (a) 7 (b) 25 (c) 6 (d) 5
  14. 14.How far is the point (6, 8) from the origin (0, 0)? (a) 10 (b) 100 (c) 14 (d) 11
  15. 15.What is the midpoint of the line joining (3, 8) and (7, 16)? (a) (12, 5) (b) (10, 24) (c) (5, 12) (d) (2, 4)
  16. 16.In which quadrant does the point (−1, 2) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  17. 17.What is the distance between the points (3, 19) and (8, 7)? (a) 13 (b) 17 (c) 14 (d) 169
  18. 18.What is the distance between the points (8, 1) and (13, 13)? (a) 14 (b) 169 (c) 13 (d) 17
  19. 19.How far is the point (12, 16) from the origin (0, 0)? (a) 20 (b) 21 (c) 400 (d) 28
  20. 20.What is the distance between the points (1, 6) and (4, 10)? (a) 25 (b) 6 (c) 7 (d) 5
  21. 21.What is the distance between the points (3, 8) and (11, 14)? (a) 10 (b) 14 (c) 100 (d) 11
  22. 22.In which quadrant does the point (6, 2) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  23. 23.In which quadrant does the point (−4, −9) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  24. 24.What is the midpoint of the line joining (10, 5) and (16, 13)? (a) (13, 9) (b) (9, 13) (c) (26, 18) (d) (3, 4)
  25. 25.In which quadrant does the point (−2, 1) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
  26. 26.What is the midpoint of the line joining (3, 6) and (9, 14)? (a) (10, 6) (b) (3, 4) (c) (12, 20) (d) (6, 10)
  27. 27.How far is the point (24, 7) from the origin (0, 0)? (a) 625 (b) 31 (c) 26 (d) 25
  28. 28.In which quadrant does the point (8, −6) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  29. 29.What is the midpoint of the line joining (6, 7) and (14, 1)? (a) (4, 3) (b) (20, 8) (c) (4, 10) (d) (10, 4)
  30. 30.What is the distance between the points (8, 5) and (24, 17)? (a) 20 (b) 21 (c) 400 (d) 28
  31. 31.What is the distance between the points (3, 12) and (18, 4)? (a) 18 (b) 289 (c) 17 (d) 23
  32. 32.What is the distance between the points (3, 9) and (19, 21)? (a) 28 (b) 400 (c) 21 (d) 20
  33. 33.In which quadrant does the point (5, 3) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  34. 34.What is the distance between the points (2, 0) and (17, 8)? (a) 17 (b) 18 (c) 289 (d) 23
  35. 35.What is the distance between the points (3, 16) and (12, 4)? (a) 225 (b) 15 (c) 16 (d) 21
  36. 36.In which quadrant does the point (−3, 2) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  37. 37.What is the distance between the points (6, 6) and (22, 18)? (a) 28 (b) 400 (c) 21 (d) 20
  38. 38.What is the distance between the points (1, 1) and (9, 7)? (a) 11 (b) 10 (c) 100 (d) 14
  39. 39.In which quadrant does the point (−5, 1) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  40. 40.What is the midpoint of the line joining (0, 2) and (2, 4)? (a) (3, 1) (b) (1, 3) (c) (1, 1) (d) (2, 6)

Answer key

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

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