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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 58 · 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 (2, 10) and (12, 22)? (a) (16, 7) (b) (14, 32) (c) (7, 16) (d) (5, 6)
  2. 2.In which quadrant does the point (−8, −4) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  3. 3.In which quadrant does the point (9, −8) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  4. 4.How far is the point (9, 12) from the origin (0, 0)? (a) 16 (b) 21 (c) 225 (d) 15
  5. 5.What is the midpoint of the line joining (7, 18) and (11, 6)? (a) (2, 6) (b) (9, 12) (c) (12, 9) (d) (18, 24)
  6. 6.How far is the point (5, 12) from the origin (0, 0)? (a) 13 (b) 14 (c) 169 (d) 17
  7. 7.What is the midpoint of the line joining (5, 7) and (7, 5)? (a) (12, 12) (b) (6, 6) (c) (7, 6) (d) (1, 1)
  8. 8.What is the midpoint of the line joining (0, 19) and (6, 9)? (a) (6, 28) (b) (14, 3) (c) (3, 5) (d) (3, 14)
  9. 9.In which quadrant does the point (−3, 2) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  10. 10.What is the midpoint of the line joining (10, 19) and (22, 9)? (a) (16, 14) (b) (32, 28) (c) (14, 16) (d) (6, 5)
  11. 11.What is the distance between the points (2, 9) and (14, 18)? (a) 21 (b) 16 (c) 225 (d) 15
  12. 12.In which quadrant does the point (4, 1) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  13. 13.What is the midpoint of the line joining (4, 12) and (10, 10)? (a) (14, 22) (b) (3, 1) (c) (11, 7) (d) (7, 11)
  14. 14.What is the distance between the points (3, 7) and (18, 15)? (a) 18 (b) 17 (c) 289 (d) 23
  15. 15.What is the midpoint of the line joining (1, 4) and (11, 0)? (a) (12, 4) (b) (6, 2) (c) (2, 6) (d) (5, 2)
  16. 16.What is the midpoint of the line joining (6, 10) and (8, 16)? (a) (13, 7) (b) (7, 13) (c) (1, 3) (d) (14, 26)
  17. 17.What is the distance between the points (6, 6) and (12, 14)? (a) 10 (b) 100 (c) 11 (d) 14
  18. 18.What is the midpoint of the line joining (10, 9) and (22, 5)? (a) (6, 2) (b) (16, 7) (c) (32, 14) (d) (7, 16)
  19. 19.What is the distance between the points (1, 10) and (7, 2)? (a) 100 (b) 11 (c) 14 (d) 10
  20. 20.What is the distance between the points (2, 7) and (26, 0)? (a) 31 (b) 25 (c) 625 (d) 26
  21. 21.What is the distance between the points (7, 8) and (13, 16)? (a) 11 (b) 10 (c) 14 (d) 100
  22. 22.What is the distance between the points (1, 2) and (13, 7)? (a) 17 (b) 13 (c) 169 (d) 14
  23. 23.How far is the point (24, 7) from the origin (0, 0)? (a) 31 (b) 625 (c) 26 (d) 25
  24. 24.What is the midpoint of the line joining (3, 16) and (11, 8)? (a) (14, 24) (b) (7, 12) (c) (12, 7) (d) (4, 4)
  25. 25.What is the distance between the points (0, 9) and (3, 5)? (a) 5 (b) 6 (c) 25 (d) 7
  26. 26.What is the midpoint of the line joining (2, 9) and (12, 7)? (a) (14, 16) (b) (5, 1) (c) (7, 8) (d) (8, 7)
  27. 27.What is the distance between the points (2, 6) and (14, 15)? (a) 225 (b) 16 (c) 21 (d) 15
  28. 28.What is the distance between the points (3, 20) and (19, 8)? (a) 400 (b) 21 (c) 28 (d) 20
  29. 29.What is the distance between the points (7, 3) and (19, 19)? (a) 20 (b) 21 (c) 28 (d) 400
  30. 30.What is the midpoint of the line joining (6, 10) and (10, 6)? (a) (16, 16) (b) (9, 8) (c) (2, 2) (d) (8, 8)
  31. 31.What is the distance between the points (1, 5) and (9, 11)? (a) 14 (b) 10 (c) 100 (d) 11
  32. 32.In which quadrant does the point (−8, 3) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  33. 33.In which quadrant does the point (−4, 1) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
  34. 34.What is the midpoint of the line joining (1, 0) and (13, 12)? (a) (6, 6) (b) (14, 12) (c) (6, 7) (d) (7, 6)
  35. 35.What is the distance between the points (3, 22) and (15, 6)? (a) 400 (b) 20 (c) 21 (d) 28
  36. 36.In which quadrant does the point (−2, 1) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  37. 37.In which quadrant does the point (5, 3) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  38. 38.What is the distance between the points (1, 11) and (16, 3)? (a) 18 (b) 289 (c) 23 (d) 17
  39. 39.What is the distance between the points (5, 11) and (11, 3)? (a) 10 (b) 100 (c) 14 (d) 11
  40. 40.What is the midpoint of the line joining (1, 6) and (3, 2)? (a) (1, 2) (b) (2, 4) (c) (4, 8) (d) (4, 2)

Answer key

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

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