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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 220 · 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 distance between the points (6, 5) and (9, 9)? (a) 7 (b) 6 (c) 25 (d) 5
  2. 2.What is the distance between the points (3, 2) and (18, 10)? (a) 18 (b) 23 (c) 289 (d) 17
  3. 3.In which quadrant does the point (−1, −7) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  4. 4.In which quadrant does the point (1, 2) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  5. 5.What is the distance between the points (2, 0) and (14, 16)? (a) 400 (b) 20 (c) 21 (d) 28
  6. 6.What is the distance between the points (4, 0) and (7, 4)? (a) 7 (b) 25 (c) 6 (d) 5
  7. 7.What is the midpoint of the line joining (10, 4) and (12, 10)? (a) (1, 3) (b) (7, 11) (c) (22, 14) (d) (11, 7)
  8. 8.What is the midpoint of the line joining (9, 2) and (17, 12)? (a) (4, 5) (b) (7, 13) (c) (13, 7) (d) (26, 14)
  9. 9.How far is the point (12, 16) from the origin (0, 0)? (a) 28 (b) 21 (c) 400 (d) 20
  10. 10.How far is the point (7, 24) from the origin (0, 0)? (a) 31 (b) 25 (c) 26 (d) 625
  11. 11.What is the midpoint of the line joining (0, 17) and (8, 9)? (a) (8, 26) (b) (4, 13) (c) (13, 4) (d) (4, 4)
  12. 12.What is the midpoint of the line joining (4, 9) and (16, 19)? (a) (14, 10) (b) (20, 28) (c) (6, 5) (d) (10, 14)
  13. 13.How far is the point (16, 12) from the origin (0, 0)? (a) 21 (b) 28 (c) 20 (d) 400
  14. 14.What is the midpoint of the line joining (3, 10) and (15, 0)? (a) (18, 10) (b) (5, 9) (c) (6, 5) (d) (9, 5)
  15. 15.What is the distance between the points (9, 12) and (33, 5)? (a) 625 (b) 25 (c) 31 (d) 26
  16. 16.How far is the point (9, 12) from the origin (0, 0)? (a) 225 (b) 21 (c) 16 (d) 15
  17. 17.How far is the point (12, 9) from the origin (0, 0)? (a) 21 (b) 15 (c) 225 (d) 16
  18. 18.What is the midpoint of the line joining (0, 8) and (2, 14)? (a) (1, 3) (b) (11, 1) (c) (1, 11) (d) (2, 22)
  19. 19.In which quadrant does the point (−2, 4) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  20. 20.In which quadrant does the point (−7, 8) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  21. 21.What is the midpoint of the line joining (4, 0) and (14, 2)? (a) (1, 9) (b) (5, 1) (c) (18, 2) (d) (9, 1)
  22. 22.What is the midpoint of the line joining (0, 5) and (10, 1)? (a) (5, 2) (b) (10, 6) (c) (3, 5) (d) (5, 3)
  23. 23.In which quadrant does the point (8, −3) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  24. 24.How far is the point (3, 4) from the origin (0, 0)? (a) 6 (b) 5 (c) 25 (d) 7
  25. 25.What is the midpoint of the line joining (8, 2) and (14, 8)? (a) (22, 10) (b) (3, 3) (c) (11, 5) (d) (5, 11)
  26. 26.What is the midpoint of the line joining (0, 15) and (4, 3)? (a) (2, 9) (b) (9, 2) (c) (4, 18) (d) (2, 6)
  27. 27.In which quadrant does the point (−4, 4) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  28. 28.In which quadrant does the point (4, 8) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  29. 29.What is the distance between the points (2, 5) and (5, 9)? (a) 25 (b) 7 (c) 6 (d) 5
  30. 30.In which quadrant does the point (1, 8) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  31. 31.What is the distance between the points (9, 2) and (21, 18)? (a) 400 (b) 21 (c) 28 (d) 20
  32. 32.In which quadrant does the point (4, 2) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  33. 33.In which quadrant does the point (8, −7) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  34. 34.What is the midpoint of the line joining (2, 1) and (10, 7)? (a) (12, 8) (b) (4, 3) (c) (6, 4) (d) (4, 6)
  35. 35.What is the distance between the points (8, 2) and (16, 17)? (a) 23 (b) 289 (c) 17 (d) 18
  36. 36.What is the distance between the points (3, 0) and (6, 4)? (a) 7 (b) 6 (c) 5 (d) 25
  37. 37.What is the distance between the points (9, 9) and (15, 1)? (a) 14 (b) 100 (c) 11 (d) 10
  38. 38.In which quadrant does the point (−2, 1) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  39. 39.What is the midpoint of the line joining (6, 13) and (10, 5)? (a) (16, 18) (b) (8, 9) (c) (9, 8) (d) (2, 4)
  40. 40.What is the midpoint of the line joining (1, 19) and (5, 9)? (a) (2, 5) (b) (3, 14) (c) (14, 3) (d) (6, 28)

Answer key

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

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