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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 317 · 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 midpoint of the line joining (0, 14) and (4, 6)? (a) (2, 4) (b) (10, 2) (c) (4, 20) (d) (2, 10)
  2. 2.How far is the point (8, 15) from the origin (0, 0)? (a) 23 (b) 289 (c) 18 (d) 17
  3. 3.What is the midpoint of the line joining (2, 6) and (10, 0)? (a) (12, 6) (b) (6, 3) (c) (4, 3) (d) (3, 6)
  4. 4.How far is the point (5, 12) from the origin (0, 0)? (a) 17 (b) 14 (c) 169 (d) 13
  5. 5.What is the distance between the points (2, 3) and (26, 10)? (a) 625 (b) 31 (c) 25 (d) 26
  6. 6.In which quadrant does the point (−3, −8) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  7. 7.What is the distance between the points (0, 13) and (12, 8)? (a) 13 (b) 17 (c) 169 (d) 14
  8. 8.In which quadrant does the point (7, 5) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  9. 9.How far is the point (8, 6) from the origin (0, 0)? (a) 100 (b) 10 (c) 14 (d) 11
  10. 10.How far is the point (12, 16) from the origin (0, 0)? (a) 28 (b) 400 (c) 21 (d) 20
  11. 11.In which quadrant does the point (3, 9) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  12. 12.What is the distance between the points (3, 3) and (7, 6)? (a) 7 (b) 6 (c) 25 (d) 5
  13. 13.What is the distance between the points (8, 18) and (20, 2)? (a) 400 (b) 21 (c) 20 (d) 28
  14. 14.In which quadrant does the point (−6, −3) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  15. 15.What is the midpoint of the line joining (8, 20) and (12, 8)? (a) (10, 14) (b) (2, 6) (c) (20, 28) (d) (14, 10)
  16. 16.In which quadrant does the point (−2, −4) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  17. 17.What is the midpoint of the line joining (6, 7) and (12, 11)? (a) (18, 18) (b) (3, 2) (c) (9, 9) (d) (10, 9)
  18. 18.What is the midpoint of the line joining (9, 2) and (21, 4)? (a) (15, 3) (b) (6, 1) (c) (30, 6) (d) (3, 15)
  19. 19.What is the midpoint of the line joining (6, 2) and (16, 10)? (a) (6, 11) (b) (5, 4) (c) (22, 12) (d) (11, 6)
  20. 20.What is the distance between the points (1, 2) and (9, 8)? (a) 14 (b) 10 (c) 100 (d) 11
  21. 21.How far is the point (12, 9) from the origin (0, 0)? (a) 225 (b) 15 (c) 21 (d) 16
  22. 22.What is the distance between the points (1, 2) and (4, 6)? (a) 7 (b) 6 (c) 25 (d) 5
  23. 23.How far is the point (16, 12) from the origin (0, 0)? (a) 28 (b) 21 (c) 400 (d) 20
  24. 24.What is the distance between the points (7, 2) and (14, 26)? (a) 26 (b) 25 (c) 625 (d) 31
  25. 25.What is the midpoint of the line joining (8, 12) and (10, 8)? (a) (1, 2) (b) (18, 20) (c) (10, 9) (d) (9, 10)
  26. 26.In which quadrant does the point (−4, −6) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  27. 27.In which quadrant does the point (1, 9) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  28. 28.What is the distance between the points (2, 16) and (14, 0)? (a) 400 (b) 21 (c) 28 (d) 20
  29. 29.In which quadrant does the point (−9, 8) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  30. 30.How far is the point (24, 7) from the origin (0, 0)? (a) 25 (b) 625 (c) 26 (d) 31
  31. 31.In which quadrant does the point (−7, −1) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  32. 32.In which quadrant does the point (−4, 8) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  33. 33.What is the midpoint of the line joining (10, 3) and (16, 7)? (a) (26, 10) (b) (13, 5) (c) (3, 2) (d) (5, 13)
  34. 34.In which quadrant does the point (4, 4) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  35. 35.What is the midpoint of the line joining (7, 3) and (17, 9)? (a) (24, 12) (b) (6, 12) (c) (12, 6) (d) (5, 3)
  36. 36.What is the midpoint of the line joining (2, 5) and (8, 15)? (a) (5, 10) (b) (10, 5) (c) (3, 5) (d) (10, 20)
  37. 37.What is the distance between the points (1, 1) and (17, 13)? (a) 20 (b) 400 (c) 28 (d) 21
  38. 38.What is the midpoint of the line joining (6, 13) and (12, 1)? (a) (3, 6) (b) (9, 7) (c) (18, 14) (d) (7, 9)
  39. 39.How far is the point (6, 8) from the origin (0, 0)? (a) 10 (b) 14 (c) 100 (d) 11
  40. 40.In which quadrant does the point (8, −3) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant

Answer key

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

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