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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 528 · 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, 8) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  2. 2.How far is the point (3, 4) from the origin (0, 0)? (a) 7 (b) 6 (c) 5 (d) 25
  3. 3.In which quadrant does the point (8, 3) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  4. 4.What is the distance between the points (0, 0) and (8, 6)? (a) 11 (b) 100 (c) 14 (d) 10
  5. 5.How far is the point (12, 16) from the origin (0, 0)? (a) 28 (b) 20 (c) 400 (d) 21
  6. 6.What is the distance between the points (3, 7) and (10, 31)? (a) 31 (b) 26 (c) 25 (d) 625
  7. 7.How far is the point (4, 3) from the origin (0, 0)? (a) 6 (b) 5 (c) 25 (d) 7
  8. 8.In which quadrant does the point (6, 5) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  9. 9.What is the distance between the points (6, 6) and (14, 0)? (a) 100 (b) 10 (c) 11 (d) 14
  10. 10.How far is the point (12, 9) from the origin (0, 0)? (a) 225 (b) 16 (c) 21 (d) 15
  11. 11.What is the distance between the points (1, 0) and (16, 8)? (a) 18 (b) 23 (c) 289 (d) 17
  12. 12.In which quadrant does the point (−6, −6) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  13. 13.How far is the point (9, 12) from the origin (0, 0)? (a) 16 (b) 225 (c) 15 (d) 21
  14. 14.What is the midpoint of the line joining (10, 11) and (16, 7)? (a) (13, 9) (b) (3, 2) (c) (9, 13) (d) (26, 18)
  15. 15.What is the distance between the points (6, 3) and (14, 18)? (a) 289 (b) 17 (c) 23 (d) 18
  16. 16.What is the distance between the points (9, 2) and (21, 7)? (a) 14 (b) 169 (c) 13 (d) 17
  17. 17.What is the midpoint of the line joining (3, 3) and (7, 15)? (a) (10, 18) (b) (9, 5) (c) (2, 6) (d) (5, 9)
  18. 18.In which quadrant does the point (−1, −3) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  19. 19.What is the midpoint of the line joining (3, 13) and (7, 1)? (a) (5, 7) (b) (2, 6) (c) (10, 14) (d) (7, 5)
  20. 20.What is the distance between the points (2, 16) and (18, 4)? (a) 21 (b) 400 (c) 28 (d) 20
  21. 21.What is the midpoint of the line joining (0, 8) and (6, 20)? (a) (14, 3) (b) (3, 6) (c) (6, 28) (d) (3, 14)
  22. 22.In which quadrant does the point (−2, 1) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  23. 23.How far is the point (5, 12) from the origin (0, 0)? (a) 169 (b) 14 (c) 17 (d) 13
  24. 24.What is the midpoint of the line joining (10, 8) and (12, 18)? (a) (13, 11) (b) (1, 5) (c) (11, 13) (d) (22, 26)
  25. 25.What is the distance between the points (6, 10) and (12, 2)? (a) 14 (b) 100 (c) 10 (d) 11
  26. 26.In which quadrant does the point (5, 4) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  27. 27.How far is the point (8, 6) from the origin (0, 0)? (a) 100 (b) 14 (c) 10 (d) 11
  28. 28.What is the distance between the points (4, 8) and (28, 15)? (a) 25 (b) 31 (c) 26 (d) 625
  29. 29.What is the distance between the points (2, 6) and (17, 14)? (a) 23 (b) 17 (c) 18 (d) 289
  30. 30.In which quadrant does the point (5, 3) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  31. 31.What is the distance between the points (5, 4) and (17, 20)? (a) 28 (b) 400 (c) 21 (d) 20
  32. 32.What is the distance between the points (1, 6) and (17, 18)? (a) 28 (b) 400 (c) 21 (d) 20
  33. 33.What is the midpoint of the line joining (5, 14) and (7, 2)? (a) (12, 16) (b) (8, 6) (c) (1, 6) (d) (6, 8)
  34. 34.In which quadrant does the point (−3, 3) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  35. 35.What is the distance between the points (6, 14) and (11, 2)? (a) 17 (b) 169 (c) 13 (d) 14
  36. 36.What is the midpoint of the line joining (2, 5) and (6, 15)? (a) (10, 4) (b) (2, 5) (c) (4, 10) (d) (8, 20)
  37. 37.In which quadrant does the point (−1, −2) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  38. 38.What is the distance between the points (9, 5) and (17, 20)? (a) 17 (b) 18 (c) 289 (d) 23
  39. 39.What is the distance between the points (0, 8) and (16, 20)? (a) 400 (b) 28 (c) 21 (d) 20
  40. 40.What is the midpoint of the line joining (0, 9) and (4, 11)? (a) (4, 20) (b) (2, 10) (c) (2, 1) (d) (10, 2)

Answer key

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

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