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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 269 · 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 (12, 9) from the origin (0, 0)? (a) 15 (b) 225 (c) 16 (d) 21
  2. 2.In which quadrant does the point (−1, −6) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  3. 3.What is the distance between the points (9, 16) and (25, 4)? (a) 21 (b) 400 (c) 28 (d) 20
  4. 4.What is the distance between the points (2, 14) and (14, 5)? (a) 225 (b) 16 (c) 15 (d) 21
  5. 5.What is the distance between the points (7, 31) and (14, 7)? (a) 625 (b) 31 (c) 26 (d) 25
  6. 6.How far is the point (8, 15) from the origin (0, 0)? (a) 18 (b) 289 (c) 23 (d) 17
  7. 7.How far is the point (8, 6) from the origin (0, 0)? (a) 11 (b) 100 (c) 10 (d) 14
  8. 8.In which quadrant does the point (2, 8) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  9. 9.What is the midpoint of the line joining (9, 22) and (19, 10)? (a) (5, 6) (b) (28, 32) (c) (14, 16) (d) (16, 14)
  10. 10.In which quadrant does the point (−2, 4) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  11. 11.How far is the point (15, 8) from the origin (0, 0)? (a) 18 (b) 289 (c) 17 (d) 23
  12. 12.What is the distance between the points (1, 9) and (17, 21)? (a) 21 (b) 400 (c) 28 (d) 20
  13. 13.What is the distance between the points (7, 17) and (22, 9)? (a) 17 (b) 289 (c) 23 (d) 18
  14. 14.In which quadrant does the point (6, −6) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  15. 15.In which quadrant does the point (−7, 3) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  16. 16.What is the midpoint of the line joining (3, 7) and (7, 9)? (a) (8, 5) (b) (5, 8) (c) (2, 1) (d) (10, 16)
  17. 17.What is the midpoint of the line joining (3, 9) and (15, 15)? (a) (6, 3) (b) (9, 12) (c) (12, 9) (d) (18, 24)
  18. 18.In which quadrant does the point (5, 3) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  19. 19.How far is the point (5, 12) from the origin (0, 0)? (a) 169 (b) 17 (c) 13 (d) 14
  20. 20.In which quadrant does the point (8, 8) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  21. 21.What is the distance between the points (4, 1) and (16, 17)? (a) 20 (b) 21 (c) 28 (d) 400
  22. 22.What is the midpoint of the line joining (2, 8) and (4, 18)? (a) (13, 3) (b) (1, 5) (c) (3, 13) (d) (6, 26)
  23. 23.What is the midpoint of the line joining (0, 2) and (8, 6)? (a) (4, 2) (b) (8, 8) (c) (5, 4) (d) (4, 4)
  24. 24.In which quadrant does the point (7, −9) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  25. 25.In which quadrant does the point (2, 4) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  26. 26.What is the midpoint of the line joining (0, 12) and (4, 0)? (a) (3, 6) (b) (4, 12) (c) (2, 6) (d) (6, 2)
  27. 27.In which quadrant does the point (−4, −4) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  28. 28.What is the midpoint of the line joining (9, 12) and (15, 10)? (a) (11, 12) (b) (3, 1) (c) (24, 22) (d) (12, 11)
  29. 29.What is the distance between the points (0, 18) and (5, 6)? (a) 169 (b) 14 (c) 13 (d) 17
  30. 30.What is the distance between the points (2, 32) and (9, 8)? (a) 625 (b) 26 (c) 25 (d) 31
  31. 31.What is the distance between the points (6, 6) and (18, 15)? (a) 15 (b) 16 (c) 21 (d) 225
  32. 32.What is the midpoint of the line joining (10, 7) and (14, 3)? (a) (12, 5) (b) (2, 2) (c) (5, 12) (d) (24, 10)
  33. 33.What is the midpoint of the line joining (5, 19) and (11, 9)? (a) (8, 14) (b) (14, 8) (c) (3, 5) (d) (16, 28)
  34. 34.What is the distance between the points (8, 5) and (12, 2)? (a) 5 (b) 25 (c) 7 (d) 6
  35. 35.In which quadrant does the point (1, −5) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
  36. 36.In which quadrant does the point (8, 1) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  37. 37.What is the distance between the points (3, 9) and (9, 17)? (a) 14 (b) 11 (c) 10 (d) 100
  38. 38.What is the midpoint of the line joining (9, 22) and (13, 10)? (a) (22, 32) (b) (2, 6) (c) (16, 11) (d) (11, 16)
  39. 39.What is the distance between the points (1, 21) and (6, 9)? (a) 169 (b) 14 (c) 17 (d) 13
  40. 40.What is the midpoint of the line joining (1, 13) and (13, 5)? (a) (6, 4) (b) (9, 7) (c) (14, 18) (d) (7, 9)

Answer key

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

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