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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 925 · 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.In which quadrant does the point (−3, −6) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  2. 2.What is the midpoint of the line joining (4, 4) and (14, 6)? (a) (5, 1) (b) (5, 9) (c) (18, 10) (d) (9, 5)
  3. 3.What is the midpoint of the line joining (6, 11) and (16, 5)? (a) (5, 3) (b) (8, 11) (c) (11, 8) (d) (22, 16)
  4. 4.How far is the point (15, 8) from the origin (0, 0)? (a) 289 (b) 17 (c) 23 (d) 18
  5. 5.What is the midpoint of the line joining (6, 6) and (10, 18)? (a) (16, 24) (b) (12, 8) (c) (8, 12) (d) (2, 6)
  6. 6.What is the midpoint of the line joining (1, 8) and (5, 2)? (a) (2, 3) (b) (6, 10) (c) (5, 3) (d) (3, 5)
  7. 7.In which quadrant does the point (−6, 5) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  8. 8.How far is the point (8, 6) from the origin (0, 0)? (a) 100 (b) 10 (c) 11 (d) 14
  9. 9.What is the distance between the points (0, 13) and (15, 5)? (a) 289 (b) 18 (c) 23 (d) 17
  10. 10.How far is the point (12, 5) from the origin (0, 0)? (a) 14 (b) 17 (c) 13 (d) 169
  11. 11.How far is the point (7, 24) from the origin (0, 0)? (a) 625 (b) 26 (c) 31 (d) 25
  12. 12.In which quadrant does the point (−2, −8) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  13. 13.What is the distance between the points (4, 16) and (16, 7)? (a) 16 (b) 225 (c) 15 (d) 21
  14. 14.What is the midpoint of the line joining (8, 12) and (20, 2)? (a) (6, 5) (b) (7, 14) (c) (28, 14) (d) (14, 7)
  15. 15.What is the midpoint of the line joining (4, 8) and (8, 20)? (a) (14, 6) (b) (12, 28) (c) (2, 6) (d) (6, 14)
  16. 16.What is the midpoint of the line joining (2, 18) and (6, 6)? (a) (12, 4) (b) (2, 6) (c) (4, 12) (d) (8, 24)
  17. 17.How far is the point (12, 9) from the origin (0, 0)? (a) 21 (b) 16 (c) 225 (d) 15
  18. 18.In which quadrant does the point (−5, 4) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  19. 19.In which quadrant does the point (8, −3) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  20. 20.What is the distance between the points (8, 9) and (20, 18)? (a) 16 (b) 21 (c) 15 (d) 225
  21. 21.What is the midpoint of the line joining (8, 7) and (14, 19)? (a) (3, 6) (b) (13, 11) (c) (11, 13) (d) (22, 26)
  22. 22.What is the distance between the points (8, 6) and (16, 0)? (a) 10 (b) 14 (c) 11 (d) 100
  23. 23.How far is the point (16, 12) from the origin (0, 0)? (a) 20 (b) 28 (c) 400 (d) 21
  24. 24.In which quadrant does the point (−2, 7) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  25. 25.What is the midpoint of the line joining (2, 2) and (8, 14)? (a) (8, 5) (b) (3, 6) (c) (5, 8) (d) (10, 16)
  26. 26.What is the midpoint of the line joining (10, 18) and (14, 8)? (a) (2, 5) (b) (13, 12) (c) (12, 13) (d) (24, 26)
  27. 27.How far is the point (6, 8) from the origin (0, 0)? (a) 10 (b) 14 (c) 11 (d) 100
  28. 28.In which quadrant does the point (−3, 2) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  29. 29.How far is the point (12, 16) from the origin (0, 0)? (a) 400 (b) 21 (c) 20 (d) 28
  30. 30.What is the distance between the points (7, 16) and (19, 7)? (a) 15 (b) 21 (c) 225 (d) 16
  31. 31.In which quadrant does the point (5, 3) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  32. 32.What is the distance between the points (8, 0) and (20, 9)? (a) 225 (b) 15 (c) 16 (d) 21
  33. 33.What is the midpoint of the line joining (3, 9) and (5, 5)? (a) (7, 4) (b) (8, 14) (c) (4, 7) (d) (1, 2)
  34. 34.How far is the point (3, 4) from the origin (0, 0)? (a) 5 (b) 7 (c) 25 (d) 6
  35. 35.How far is the point (4, 3) from the origin (0, 0)? (a) 7 (b) 25 (c) 6 (d) 5
  36. 36.What is the distance between the points (7, 14) and (31, 7)? (a) 25 (b) 625 (c) 26 (d) 31
  37. 37.In which quadrant does the point (9, 1) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  38. 38.What is the midpoint of the line joining (6, 4) and (12, 16)? (a) (9, 10) (b) (10, 9) (c) (18, 20) (d) (3, 6)
  39. 39.How far is the point (9, 12) from the origin (0, 0)? (a) 21 (b) 225 (c) 15 (d) 16
  40. 40.What is the distance between the points (0, 23) and (12, 7)? (a) 20 (b) 21 (c) 400 (d) 28

Answer key

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

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