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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 633 · 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, 4) and (10, 6)? (a) (5, 1) (b) (5, 5) (c) (6, 5) (d) (10, 10)
  2. 2.What is the midpoint of the line joining (5, 6) and (17, 8)? (a) (7, 11) (b) (11, 7) (c) (22, 14) (d) (6, 1)
  3. 3.What is the distance between the points (6, 17) and (14, 2)? (a) 23 (b) 18 (c) 289 (d) 17
  4. 4.What is the midpoint of the line joining (10, 5) and (12, 17)? (a) (12, 11) (b) (22, 22) (c) (11, 11) (d) (1, 6)
  5. 5.How far is the point (16, 12) from the origin (0, 0)? (a) 21 (b) 400 (c) 28 (d) 20
  6. 6.How far is the point (15, 8) from the origin (0, 0)? (a) 23 (b) 17 (c) 18 (d) 289
  7. 7.How far is the point (6, 8) from the origin (0, 0)? (a) 14 (b) 100 (c) 10 (d) 11
  8. 8.What is the distance between the points (0, 1) and (8, 7)? (a) 10 (b) 100 (c) 14 (d) 11
  9. 9.What is the distance between the points (5, 7) and (17, 2)? (a) 17 (b) 169 (c) 13 (d) 14
  10. 10.How far is the point (8, 15) from the origin (0, 0)? (a) 289 (b) 17 (c) 23 (d) 18
  11. 11.In which quadrant does the point (3, −5) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  12. 12.What is the midpoint of the line joining (9, 9) and (21, 19)? (a) (30, 28) (b) (15, 14) (c) (14, 15) (d) (6, 5)
  13. 13.What is the distance between the points (6, 14) and (18, 5)? (a) 225 (b) 21 (c) 15 (d) 16
  14. 14.What is the midpoint of the line joining (0, 7) and (2, 3)? (a) (2, 10) (b) (5, 1) (c) (1, 2) (d) (1, 5)
  15. 15.What is the distance between the points (7, 7) and (31, 0)? (a) 25 (b) 26 (c) 31 (d) 625
  16. 16.What is the distance between the points (1, 5) and (17, 17)? (a) 20 (b) 21 (c) 400 (d) 28
  17. 17.What is the midpoint of the line joining (6, 3) and (18, 9)? (a) (6, 12) (b) (24, 12) (c) (12, 6) (d) (6, 3)
  18. 18.What is the distance between the points (0, 7) and (24, 14)? (a) 31 (b) 25 (c) 26 (d) 625
  19. 19.What is the distance between the points (9, 13) and (17, 7)? (a) 10 (b) 14 (c) 11 (d) 100
  20. 20.How far is the point (12, 16) from the origin (0, 0)? (a) 400 (b) 21 (c) 28 (d) 20
  21. 21.What is the distance between the points (0, 9) and (3, 5)? (a) 5 (b) 7 (c) 25 (d) 6
  22. 22.What is the distance between the points (0, 18) and (9, 6)? (a) 225 (b) 21 (c) 15 (d) 16
  23. 23.How far is the point (4, 3) from the origin (0, 0)? (a) 6 (b) 7 (c) 25 (d) 5
  24. 24.In which quadrant does the point (−4, 6) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  25. 25.How far is the point (8, 6) from the origin (0, 0)? (a) 11 (b) 100 (c) 14 (d) 10
  26. 26.How far is the point (12, 9) from the origin (0, 0)? (a) 15 (b) 21 (c) 16 (d) 225
  27. 27.What is the distance between the points (6, 2) and (22, 14)? (a) 20 (b) 21 (c) 400 (d) 28
  28. 28.What is the midpoint of the line joining (8, 11) and (20, 1)? (a) (28, 12) (b) (14, 6) (c) (6, 14) (d) (6, 5)
  29. 29.What is the midpoint of the line joining (5, 2) and (15, 14)? (a) (5, 6) (b) (8, 10) (c) (10, 8) (d) (20, 16)
  30. 30.What is the distance between the points (6, 3) and (13, 27)? (a) 25 (b) 31 (c) 26 (d) 625
  31. 31.What is the midpoint of the line joining (0, 5) and (2, 13)? (a) (9, 1) (b) (2, 18) (c) (1, 4) (d) (1, 9)
  32. 32.What is the midpoint of the line joining (0, 13) and (4, 5)? (a) (9, 2) (b) (2, 9) (c) (2, 4) (d) (4, 18)
  33. 33.In which quadrant does the point (1, 1) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  34. 34.What is the midpoint of the line joining (2, 9) and (4, 5)? (a) (6, 14) (b) (3, 7) (c) (1, 2) (d) (7, 3)
  35. 35.How far is the point (7, 24) from the origin (0, 0)? (a) 25 (b) 31 (c) 26 (d) 625
  36. 36.What is the midpoint of the line joining (5, 6) and (9, 16)? (a) (14, 22) (b) (2, 5) (c) (11, 7) (d) (7, 11)
  37. 37.In which quadrant does the point (1, −3) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  38. 38.What is the distance between the points (6, 5) and (21, 13)? (a) 17 (b) 23 (c) 289 (d) 18
  39. 39.In which quadrant does the point (9, −6) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  40. 40.In which quadrant does the point (−5, 1) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant

Answer key

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

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