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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 993 · 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 (8, 6) from the origin (0, 0)? (a) 14 (b) 10 (c) 11 (d) 100
  2. 2.In which quadrant does the point (1, −6) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  3. 3.In which quadrant does the point (−4, 8) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  4. 4.What is the midpoint of the line joining (3, 8) and (11, 4)? (a) (14, 12) (b) (7, 6) (c) (6, 7) (d) (4, 2)
  5. 5.In which quadrant does the point (8, 9) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  6. 6.What is the distance between the points (3, 12) and (15, 3)? (a) 15 (b) 16 (c) 21 (d) 225
  7. 7.What is the distance between the points (9, 4) and (18, 16)? (a) 225 (b) 15 (c) 16 (d) 21
  8. 8.How far is the point (24, 7) from the origin (0, 0)? (a) 26 (b) 625 (c) 31 (d) 25
  9. 9.In which quadrant does the point (7, −5) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  10. 10.In which quadrant does the point (−1, −5) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  11. 11.How far is the point (12, 9) from the origin (0, 0)? (a) 21 (b) 16 (c) 15 (d) 225
  12. 12.What is the distance between the points (5, 5) and (29, 12)? (a) 625 (b) 25 (c) 31 (d) 26
  13. 13.What is the distance between the points (9, 28) and (16, 4)? (a) 625 (b) 25 (c) 26 (d) 31
  14. 14.How far is the point (12, 16) from the origin (0, 0)? (a) 28 (b) 21 (c) 400 (d) 20
  15. 15.In which quadrant does the point (−1, 5) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  16. 16.What is the distance between the points (1, 9) and (17, 21)? (a) 400 (b) 20 (c) 28 (d) 21
  17. 17.What is the distance between the points (5, 8) and (11, 0)? (a) 10 (b) 14 (c) 100 (d) 11
  18. 18.What is the distance between the points (4, 4) and (10, 12)? (a) 100 (b) 11 (c) 10 (d) 14
  19. 19.What is the midpoint of the line joining (9, 1) and (19, 11)? (a) (5, 5) (b) (28, 12) (c) (14, 6) (d) (6, 14)
  20. 20.What is the midpoint of the line joining (10, 12) and (20, 6)? (a) (9, 15) (b) (5, 3) (c) (30, 18) (d) (15, 9)
  21. 21.What is the distance between the points (8, 16) and (13, 4)? (a) 14 (b) 169 (c) 13 (d) 17
  22. 22.What is the distance between the points (6, 2) and (18, 11)? (a) 15 (b) 21 (c) 16 (d) 225
  23. 23.How far is the point (6, 8) from the origin (0, 0)? (a) 14 (b) 10 (c) 11 (d) 100
  24. 24.In which quadrant does the point (−5, −2) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  25. 25.What is the distance between the points (8, 1) and (24, 13)? (a) 21 (b) 20 (c) 28 (d) 400
  26. 26.In which quadrant does the point (−5, −8) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  27. 27.What is the midpoint of the line joining (5, 5) and (13, 1)? (a) (4, 2) (b) (9, 3) (c) (18, 6) (d) (3, 9)
  28. 28.What is the distance between the points (7, 5) and (19, 0)? (a) 14 (b) 169 (c) 13 (d) 17
  29. 29.What is the distance between the points (0, 8) and (6, 16)? (a) 10 (b) 11 (c) 14 (d) 100
  30. 30.What is the distance between the points (5, 8) and (9, 11)? (a) 6 (b) 7 (c) 25 (d) 5
  31. 31.What is the distance between the points (5, 7) and (17, 12)? (a) 14 (b) 169 (c) 17 (d) 13
  32. 32.What is the midpoint of the line joining (2, 4) and (6, 16)? (a) (10, 4) (b) (8, 20) (c) (4, 10) (d) (2, 6)
  33. 33.What is the distance between the points (5, 0) and (8, 4)? (a) 6 (b) 5 (c) 25 (d) 7
  34. 34.In which quadrant does the point (−6, 4) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  35. 35.What is the midpoint of the line joining (7, 15) and (17, 9)? (a) (12, 12) (b) (13, 12) (c) (24, 24) (d) (5, 3)
  36. 36.In which quadrant does the point (1, 2) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  37. 37.What is the midpoint of the line joining (4, 17) and (16, 7)? (a) (20, 24) (b) (6, 5) (c) (10, 12) (d) (12, 10)
  38. 38.How far is the point (15, 8) from the origin (0, 0)? (a) 18 (b) 17 (c) 23 (d) 289
  39. 39.What is the distance between the points (1, 4) and (8, 28)? (a) 26 (b) 31 (c) 25 (d) 625
  40. 40.What is the midpoint of the line joining (1, 12) and (9, 8)? (a) (10, 20) (b) (10, 5) (c) (4, 2) (d) (5, 10)

Answer key

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

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