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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 245 · 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.In which quadrant does the point (6, −7) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  2. 2.What is the midpoint of the line joining (2, 17) and (14, 5)? (a) (8, 11) (b) (6, 6) (c) (11, 8) (d) (16, 22)
  3. 3.How far is the point (15, 8) from the origin (0, 0)? (a) 23 (b) 18 (c) 289 (d) 17
  4. 4.What is the distance between the points (7, 0) and (22, 8)? (a) 17 (b) 18 (c) 23 (d) 289
  5. 5.What is the midpoint of the line joining (0, 3) and (8, 5)? (a) (4, 1) (b) (8, 8) (c) (5, 4) (d) (4, 4)
  6. 6.In which quadrant does the point (9, −4) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  7. 7.In which quadrant does the point (2, −8) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  8. 8.What is the distance between the points (9, 15) and (25, 3)? (a) 28 (b) 400 (c) 21 (d) 20
  9. 9.What is the midpoint of the line joining (2, 20) and (6, 10)? (a) (4, 15) (b) (2, 5) (c) (8, 30) (d) (15, 4)
  10. 10.What is the distance between the points (1, 4) and (4, 0)? (a) 7 (b) 25 (c) 6 (d) 5
  11. 11.What is the midpoint of the line joining (0, 9) and (2, 11)? (a) (1, 1) (b) (1, 10) (c) (10, 1) (d) (2, 20)
  12. 12.In which quadrant does the point (2, 4) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  13. 13.What is the midpoint of the line joining (6, 5) and (14, 11)? (a) (4, 3) (b) (10, 8) (c) (20, 16) (d) (8, 10)
  14. 14.What is the distance between the points (6, 16) and (18, 7)? (a) 21 (b) 16 (c) 15 (d) 225
  15. 15.What is the midpoint of the line joining (6, 7) and (12, 9)? (a) (8, 9) (b) (18, 16) (c) (3, 1) (d) (9, 8)
  16. 16.What is the midpoint of the line joining (2, 10) and (4, 6)? (a) (8, 3) (b) (6, 16) (c) (3, 8) (d) (1, 2)
  17. 17.What is the midpoint of the line joining (0, 2) and (4, 4)? (a) (3, 2) (b) (4, 6) (c) (2, 3) (d) (2, 1)
  18. 18.What is the distance between the points (3, 6) and (15, 15)? (a) 16 (b) 21 (c) 225 (d) 15
  19. 19.In which quadrant does the point (−7, −8) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  20. 20.What is the distance between the points (5, 6) and (21, 18)? (a) 400 (b) 20 (c) 21 (d) 28
  21. 21.In which quadrant does the point (9, 6) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  22. 22.What is the distance between the points (1, 10) and (9, 4)? (a) 11 (b) 14 (c) 10 (d) 100
  23. 23.What is the distance between the points (8, 4) and (16, 10)? (a) 11 (b) 10 (c) 100 (d) 14
  24. 24.What is the distance between the points (5, 0) and (8, 4)? (a) 5 (b) 6 (c) 7 (d) 25
  25. 25.What is the distance between the points (7, 13) and (19, 8)? (a) 169 (b) 17 (c) 14 (d) 13
  26. 26.What is the distance between the points (5, 3) and (17, 8)? (a) 169 (b) 17 (c) 14 (d) 13
  27. 27.What is the distance between the points (2, 2) and (17, 10)? (a) 18 (b) 23 (c) 289 (d) 17
  28. 28.What is the distance between the points (6, 8) and (21, 16)? (a) 23 (b) 289 (c) 17 (d) 18
  29. 29.What is the distance between the points (1, 15) and (6, 3)? (a) 13 (b) 169 (c) 17 (d) 14
  30. 30.What is the midpoint of the line joining (3, 9) and (15, 17)? (a) (13, 9) (b) (6, 4) (c) (9, 13) (d) (18, 26)
  31. 31.How far is the point (4, 3) from the origin (0, 0)? (a) 25 (b) 7 (c) 6 (d) 5
  32. 32.What is the midpoint of the line joining (8, 16) and (20, 8)? (a) (28, 24) (b) (12, 14) (c) (6, 4) (d) (14, 12)
  33. 33.How far is the point (16, 12) from the origin (0, 0)? (a) 400 (b) 21 (c) 20 (d) 28
  34. 34.What is the midpoint of the line joining (0, 19) and (2, 7)? (a) (1, 6) (b) (1, 13) (c) (2, 26) (d) (13, 1)
  35. 35.In which quadrant does the point (5, −1) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  36. 36.What is the midpoint of the line joining (4, 16) and (16, 8)? (a) (12, 10) (b) (10, 12) (c) (6, 4) (d) (20, 24)
  37. 37.What is the distance between the points (2, 2) and (10, 17)? (a) 289 (b) 17 (c) 18 (d) 23
  38. 38.In which quadrant does the point (−7, 2) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  39. 39.What is the midpoint of the line joining (0, 10) and (10, 8)? (a) (5, 1) (b) (10, 18) (c) (5, 9) (d) (9, 5)
  40. 40.What is the distance between the points (2, 10) and (26, 3)? (a) 31 (b) 26 (c) 25 (d) 625

Answer key

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

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