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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 121 · 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, 7) and (14, 5)? (a) (6, 8) (b) (16, 12) (c) (6, 1) (d) (8, 6)
  2. 2.In which quadrant does the point (−1, −8) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  3. 3.What is the midpoint of the line joining (5, 7) and (9, 17)? (a) (12, 7) (b) (2, 5) (c) (14, 24) (d) (7, 12)
  4. 4.What is the distance between the points (4, 12) and (10, 4)? (a) 100 (b) 11 (c) 14 (d) 10
  5. 5.What is the distance between the points (5, 23) and (17, 7)? (a) 400 (b) 21 (c) 20 (d) 28
  6. 6.What is the distance between the points (7, 9) and (19, 18)? (a) 15 (b) 21 (c) 225 (d) 16
  7. 7.What is the distance between the points (2, 1) and (6, 4)? (a) 6 (b) 25 (c) 7 (d) 5
  8. 8.In which quadrant does the point (7, −8) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  9. 9.What is the midpoint of the line joining (6, 12) and (14, 0)? (a) (6, 10) (b) (20, 12) (c) (10, 6) (d) (4, 6)
  10. 10.What is the distance between the points (5, 16) and (14, 4)? (a) 225 (b) 21 (c) 16 (d) 15
  11. 11.How far is the point (12, 16) from the origin (0, 0)? (a) 400 (b) 28 (c) 21 (d) 20
  12. 12.What is the distance between the points (7, 3) and (19, 19)? (a) 400 (b) 21 (c) 28 (d) 20
  13. 13.What is the midpoint of the line joining (10, 3) and (22, 5)? (a) (16, 4) (b) (32, 8) (c) (4, 16) (d) (6, 1)
  14. 14.In which quadrant does the point (−8, 3) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  15. 15.What is the distance between the points (8, 6) and (32, 13)? (a) 26 (b) 31 (c) 25 (d) 625
  16. 16.What is the distance between the points (7, 24) and (15, 9)? (a) 17 (b) 23 (c) 18 (d) 289
  17. 17.How far is the point (8, 6) from the origin (0, 0)? (a) 100 (b) 11 (c) 10 (d) 14
  18. 18.What is the midpoint of the line joining (6, 12) and (12, 10)? (a) (11, 9) (b) (18, 22) (c) (9, 11) (d) (3, 1)
  19. 19.What is the distance between the points (2, 14) and (11, 2)? (a) 225 (b) 16 (c) 21 (d) 15
  20. 20.How far is the point (24, 7) from the origin (0, 0)? (a) 31 (b) 25 (c) 625 (d) 26
  21. 21.What is the distance between the points (3, 7) and (8, 19)? (a) 13 (b) 14 (c) 169 (d) 17
  22. 22.What is the midpoint of the line joining (6, 14) and (12, 10)? (a) (9, 12) (b) (18, 24) (c) (3, 2) (d) (12, 9)
  23. 23.What is the distance between the points (5, 1) and (12, 25)? (a) 31 (b) 26 (c) 25 (d) 625
  24. 24.What is the distance between the points (1, 5) and (7, 13)? (a) 14 (b) 11 (c) 10 (d) 100
  25. 25.In which quadrant does the point (8, 2) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  26. 26.What is the midpoint of the line joining (8, 1) and (18, 11)? (a) (5, 5) (b) (26, 12) (c) (6, 13) (d) (13, 6)
  27. 27.What is the distance between the points (2, 12) and (18, 0)? (a) 20 (b) 28 (c) 400 (d) 21
  28. 28.What is the midpoint of the line joining (4, 4) and (6, 10)? (a) (1, 3) (b) (7, 5) (c) (10, 14) (d) (5, 7)
  29. 29.What is the distance between the points (0, 9) and (9, 21)? (a) 225 (b) 16 (c) 21 (d) 15
  30. 30.What is the midpoint of the line joining (3, 8) and (5, 2)? (a) (5, 4) (b) (8, 10) (c) (1, 3) (d) (4, 5)
  31. 31.In which quadrant does the point (−2, 9) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  32. 32.What is the midpoint of the line joining (3, 19) and (11, 7)? (a) (7, 13) (b) (13, 7) (c) (4, 6) (d) (14, 26)
  33. 33.What is the distance between the points (0, 7) and (15, 15)? (a) 18 (b) 17 (c) 23 (d) 289
  34. 34.How far is the point (4, 3) from the origin (0, 0)? (a) 6 (b) 25 (c) 5 (d) 7
  35. 35.How far is the point (8, 15) from the origin (0, 0)? (a) 289 (b) 23 (c) 18 (d) 17
  36. 36.What is the distance between the points (4, 6) and (12, 12)? (a) 11 (b) 14 (c) 10 (d) 100
  37. 37.What is the midpoint of the line joining (1, 5) and (11, 17)? (a) (12, 22) (b) (11, 6) (c) (6, 11) (d) (5, 6)
  38. 38.What is the midpoint of the line joining (4, 0) and (14, 2)? (a) (9, 1) (b) (18, 2) (c) (1, 9) (d) (5, 1)
  39. 39.What is the midpoint of the line joining (3, 2) and (15, 0)? (a) (9, 1) (b) (1, 9) (c) (18, 2) (d) (6, 1)
  40. 40.What is the distance between the points (6, 7) and (18, 2)? (a) 14 (b) 17 (c) 13 (d) 169

Answer key

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

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