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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 137 · 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, 0) and (4, 6)? (a) (1, 3) (b) (3, 3) (c) (6, 6) (d) (4, 3)
  2. 2.What is the midpoint of the line joining (0, 12) and (4, 10)? (a) (4, 22) (b) (11, 2) (c) (2, 1) (d) (2, 11)
  3. 3.What is the midpoint of the line joining (10, 5) and (20, 1)? (a) (3, 15) (b) (5, 2) (c) (30, 6) (d) (15, 3)
  4. 4.What is the distance between the points (7, 2) and (19, 18)? (a) 20 (b) 21 (c) 400 (d) 28
  5. 5.What is the midpoint of the line joining (10, 2) and (16, 10)? (a) (13, 6) (b) (3, 4) (c) (26, 12) (d) (6, 13)
  6. 6.What is the midpoint of the line joining (9, 0) and (11, 2)? (a) (1, 10) (b) (1, 1) (c) (20, 2) (d) (10, 1)
  7. 7.What is the midpoint of the line joining (8, 8) and (10, 4)? (a) (1, 2) (b) (18, 12) (c) (9, 6) (d) (6, 9)
  8. 8.In which quadrant does the point (−8, 2) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  9. 9.What is the midpoint of the line joining (9, 4) and (21, 2)? (a) (3, 15) (b) (15, 3) (c) (30, 6) (d) (6, 1)
  10. 10.How far is the point (5, 12) from the origin (0, 0)? (a) 14 (b) 169 (c) 13 (d) 17
  11. 11.How far is the point (8, 6) from the origin (0, 0)? (a) 11 (b) 14 (c) 100 (d) 10
  12. 12.What is the midpoint of the line joining (7, 4) and (15, 14)? (a) (9, 11) (b) (4, 5) (c) (11, 9) (d) (22, 18)
  13. 13.How far is the point (3, 4) from the origin (0, 0)? (a) 5 (b) 7 (c) 6 (d) 25
  14. 14.What is the distance between the points (6, 30) and (13, 6)? (a) 25 (b) 625 (c) 26 (d) 31
  15. 15.What is the distance between the points (3, 4) and (15, 13)? (a) 21 (b) 225 (c) 15 (d) 16
  16. 16.What is the distance between the points (1, 3) and (7, 11)? (a) 14 (b) 11 (c) 10 (d) 100
  17. 17.In which quadrant does the point (−3, 5) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  18. 18.In which quadrant does the point (−9, 4) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  19. 19.What is the midpoint of the line joining (0, 7) and (6, 17)? (a) (12, 3) (b) (3, 12) (c) (6, 24) (d) (3, 5)
  20. 20.In which quadrant does the point (1, 2) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  21. 21.What is the distance between the points (1, 5) and (13, 14)? (a) 225 (b) 21 (c) 15 (d) 16
  22. 22.What is the midpoint of the line joining (0, 8) and (12, 6)? (a) (12, 14) (b) (7, 6) (c) (6, 7) (d) (6, 1)
  23. 23.What is the midpoint of the line joining (2, 9) and (8, 17)? (a) (3, 4) (b) (13, 5) (c) (5, 13) (d) (10, 26)
  24. 24.What is the midpoint of the line joining (10, 4) and (14, 14)? (a) (12, 9) (b) (24, 18) (c) (2, 5) (d) (9, 12)
  25. 25.What is the midpoint of the line joining (2, 13) and (10, 1)? (a) (4, 6) (b) (6, 7) (c) (7, 6) (d) (12, 14)
  26. 26.What is the midpoint of the line joining (0, 19) and (2, 9)? (a) (14, 1) (b) (1, 5) (c) (2, 28) (d) (1, 14)
  27. 27.What is the midpoint of the line joining (6, 11) and (8, 1)? (a) (1, 5) (b) (7, 6) (c) (6, 7) (d) (14, 12)
  28. 28.What is the distance between the points (9, 11) and (17, 5)? (a) 10 (b) 14 (c) 11 (d) 100
  29. 29.What is the distance between the points (0, 19) and (9, 7)? (a) 15 (b) 225 (c) 21 (d) 16
  30. 30.In which quadrant does the point (2, 8) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  31. 31.What is the distance between the points (4, 1) and (20, 13)? (a) 21 (b) 20 (c) 400 (d) 28
  32. 32.What is the midpoint of the line joining (10, 8) and (14, 12)? (a) (10, 12) (b) (2, 2) (c) (24, 20) (d) (12, 10)
  33. 33.What is the midpoint of the line joining (4, 9) and (12, 3)? (a) (4, 3) (b) (16, 12) (c) (8, 6) (d) (6, 8)
  34. 34.In which quadrant does the point (−5, 1) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  35. 35.What is the midpoint of the line joining (9, 3) and (15, 5)? (a) (24, 8) (b) (3, 1) (c) (12, 4) (d) (4, 12)
  36. 36.How far is the point (24, 7) from the origin (0, 0)? (a) 25 (b) 625 (c) 26 (d) 31
  37. 37.What is the distance between the points (6, 7) and (21, 15)? (a) 289 (b) 23 (c) 17 (d) 18
  38. 38.What is the distance between the points (6, 2) and (18, 11)? (a) 21 (b) 225 (c) 15 (d) 16
  39. 39.What is the midpoint of the line joining (3, 13) and (5, 7)? (a) (10, 4) (b) (1, 3) (c) (8, 20) (d) (4, 10)
  40. 40.In which quadrant does the point (−6, −1) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant

Answer key

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

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