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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 303 · 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 (7, 6) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  2. 2.What is the distance between the points (7, 13) and (23, 1)? (a) 28 (b) 400 (c) 21 (d) 20
  3. 3.How far is the point (8, 15) from the origin (0, 0)? (a) 18 (b) 17 (c) 23 (d) 289
  4. 4.How far is the point (12, 5) from the origin (0, 0)? (a) 17 (b) 169 (c) 13 (d) 14
  5. 5.How far is the point (16, 12) from the origin (0, 0)? (a) 28 (b) 400 (c) 21 (d) 20
  6. 6.In which quadrant does the point (−1, 4) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  7. 7.How far is the point (4, 3) from the origin (0, 0)? (a) 25 (b) 7 (c) 5 (d) 6
  8. 8.In which quadrant does the point (−5, −6) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  9. 9.What is the distance between the points (1, 6) and (13, 22)? (a) 28 (b) 21 (c) 20 (d) 400
  10. 10.What is the midpoint of the line joining (7, 0) and (11, 2)? (a) (1, 9) (b) (18, 2) (c) (2, 1) (d) (9, 1)
  11. 11.In which quadrant does the point (−4, 8) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  12. 12.What is the midpoint of the line joining (3, 16) and (9, 8)? (a) (3, 4) (b) (6, 12) (c) (12, 24) (d) (12, 6)
  13. 13.What is the distance between the points (9, 8) and (33, 15)? (a) 25 (b) 625 (c) 31 (d) 26
  14. 14.What is the distance between the points (0, 8) and (6, 16)? (a) 11 (b) 10 (c) 100 (d) 14
  15. 15.What is the distance between the points (0, 9) and (3, 5)? (a) 5 (b) 25 (c) 7 (d) 6
  16. 16.How far is the point (5, 12) from the origin (0, 0)? (a) 14 (b) 169 (c) 17 (d) 13
  17. 17.What is the distance between the points (3, 0) and (19, 12)? (a) 20 (b) 28 (c) 400 (d) 21
  18. 18.In which quadrant does the point (2, 3) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  19. 19.In which quadrant does the point (1, −2) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  20. 20.What is the midpoint of the line joining (5, 18) and (11, 10)? (a) (14, 8) (b) (8, 14) (c) (16, 28) (d) (3, 4)
  21. 21.In which quadrant does the point (1, −4) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
  22. 22.What is the midpoint of the line joining (2, 4) and (14, 14)? (a) (6, 5) (b) (16, 18) (c) (8, 9) (d) (9, 8)
  23. 23.What is the distance between the points (5, 7) and (12, 31)? (a) 26 (b) 25 (c) 625 (d) 31
  24. 24.In which quadrant does the point (−9, −5) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  25. 25.In which quadrant does the point (3, −7) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  26. 26.How far is the point (12, 9) from the origin (0, 0)? (a) 21 (b) 16 (c) 15 (d) 225
  27. 27.What is the distance between the points (4, 29) and (11, 5)? (a) 31 (b) 625 (c) 26 (d) 25
  28. 28.What is the distance between the points (6, 4) and (9, 8)? (a) 7 (b) 25 (c) 5 (d) 6
  29. 29.How far is the point (7, 24) from the origin (0, 0)? (a) 625 (b) 31 (c) 25 (d) 26
  30. 30.What is the midpoint of the line joining (7, 7) and (11, 11)? (a) (10, 9) (b) (18, 18) (c) (2, 2) (d) (9, 9)
  31. 31.How far is the point (24, 7) from the origin (0, 0)? (a) 625 (b) 31 (c) 25 (d) 26
  32. 32.What is the distance between the points (3, 7) and (15, 2)? (a) 169 (b) 14 (c) 17 (d) 13
  33. 33.What is the distance between the points (4, 11) and (12, 5)? (a) 10 (b) 11 (c) 14 (d) 100
  34. 34.What is the distance between the points (3, 5) and (12, 17)? (a) 21 (b) 225 (c) 16 (d) 15
  35. 35.What is the midpoint of the line joining (4, 11) and (16, 3)? (a) (20, 14) (b) (7, 10) (c) (10, 7) (d) (6, 4)
  36. 36.In which quadrant does the point (4, 6) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  37. 37.What is the midpoint of the line joining (5, 18) and (17, 8)? (a) (22, 26) (b) (13, 11) (c) (11, 13) (d) (6, 5)
  38. 38.What is the distance between the points (5, 4) and (17, 9)? (a) 14 (b) 13 (c) 17 (d) 169
  39. 39.What is the distance between the points (9, 13) and (18, 1)? (a) 225 (b) 15 (c) 16 (d) 21
  40. 40.In which quadrant does the point (−4, −3) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant

Answer key

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

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