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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 531 · 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 distance between the points (3, 13) and (15, 4)? (a) 225 (b) 16 (c) 21 (d) 15
  2. 2.What is the midpoint of the line joining (6, 9) and (8, 7)? (a) (14, 16) (b) (1, 1) (c) (7, 8) (d) (8, 7)
  3. 3.How far is the point (12, 9) from the origin (0, 0)? (a) 15 (b) 21 (c) 16 (d) 225
  4. 4.What is the midpoint of the line joining (3, 10) and (5, 22)? (a) (1, 6) (b) (16, 4) (c) (8, 32) (d) (4, 16)
  5. 5.In which quadrant does the point (−6, 5) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  6. 6.What is the midpoint of the line joining (3, 14) and (13, 6)? (a) (5, 4) (b) (10, 8) (c) (8, 10) (d) (16, 20)
  7. 7.In which quadrant does the point (3, 5) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  8. 8.In which quadrant does the point (−6, −1) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
  9. 9.What is the distance between the points (9, 2) and (25, 14)? (a) 400 (b) 21 (c) 20 (d) 28
  10. 10.How far is the point (12, 5) from the origin (0, 0)? (a) 169 (b) 17 (c) 13 (d) 14
  11. 11.What is the distance between the points (4, 6) and (7, 10)? (a) 5 (b) 6 (c) 7 (d) 25
  12. 12.What is the midpoint of the line joining (4, 9) and (8, 11)? (a) (6, 10) (b) (2, 1) (c) (10, 6) (d) (12, 20)
  13. 13.In which quadrant does the point (2, 1) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  14. 14.What is the midpoint of the line joining (1, 1) and (11, 3)? (a) (6, 2) (b) (12, 4) (c) (2, 6) (d) (5, 1)
  15. 15.In which quadrant does the point (1, −4) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  16. 16.How far is the point (7, 24) from the origin (0, 0)? (a) 25 (b) 625 (c) 31 (d) 26
  17. 17.In which quadrant does the point (8, 2) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  18. 18.What is the midpoint of the line joining (8, 14) and (14, 4)? (a) (9, 11) (b) (22, 18) (c) (3, 5) (d) (11, 9)
  19. 19.What is the distance between the points (9, 16) and (33, 9)? (a) 31 (b) 625 (c) 26 (d) 25
  20. 20.What is the distance between the points (9, 0) and (17, 6)? (a) 14 (b) 10 (c) 11 (d) 100
  21. 21.In which quadrant does the point (4, −6) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
  22. 22.What is the distance between the points (8, 7) and (20, 16)? (a) 225 (b) 16 (c) 15 (d) 21
  23. 23.In which quadrant does the point (−9, 1) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  24. 24.What is the distance between the points (6, 9) and (21, 17)? (a) 17 (b) 289 (c) 18 (d) 23
  25. 25.What is the distance between the points (2, 9) and (14, 18)? (a) 16 (b) 225 (c) 15 (d) 21
  26. 26.What is the distance between the points (2, 7) and (11, 19)? (a) 16 (b) 21 (c) 225 (d) 15
  27. 27.What is the distance between the points (0, 13) and (9, 1)? (a) 225 (b) 16 (c) 15 (d) 21
  28. 28.How far is the point (6, 8) from the origin (0, 0)? (a) 11 (b) 10 (c) 100 (d) 14
  29. 29.How far is the point (8, 15) from the origin (0, 0)? (a) 18 (b) 17 (c) 289 (d) 23
  30. 30.What is the distance between the points (1, 18) and (9, 3)? (a) 18 (b) 289 (c) 23 (d) 17
  31. 31.What is the midpoint of the line joining (9, 12) and (21, 0)? (a) (15, 6) (b) (6, 15) (c) (30, 12) (d) (6, 6)
  32. 32.In which quadrant does the point (7, 2) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  33. 33.In which quadrant does the point (5, 7) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  34. 34.In which quadrant does the point (1, 2) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  35. 35.What is the midpoint of the line joining (6, 9) and (10, 19)? (a) (2, 5) (b) (16, 28) (c) (14, 8) (d) (8, 14)
  36. 36.What is the distance between the points (4, 16) and (20, 4)? (a) 400 (b) 20 (c) 21 (d) 28
  37. 37.What is the midpoint of the line joining (7, 5) and (11, 1)? (a) (3, 9) (b) (2, 2) (c) (9, 3) (d) (18, 6)
  38. 38.In which quadrant does the point (−2, −7) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  39. 39.How far is the point (9, 12) from the origin (0, 0)? (a) 16 (b) 21 (c) 15 (d) 225
  40. 40.In which quadrant does the point (−5, −9) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant

Answer key

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

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