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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 346 · 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.How far is the point (16, 12) from the origin (0, 0)? (a) 28 (b) 21 (c) 20 (d) 400
  2. 2.How far is the point (12, 5) from the origin (0, 0)? (a) 14 (b) 13 (c) 169 (d) 17
  3. 3.What is the midpoint of the line joining (8, 19) and (20, 9)? (a) (15, 14) (b) (14, 14) (c) (6, 5) (d) (28, 28)
  4. 4.What is the midpoint of the line joining (3, 12) and (7, 6)? (a) (9, 5) (b) (5, 9) (c) (2, 3) (d) (10, 18)
  5. 5.How far is the point (3, 4) from the origin (0, 0)? (a) 7 (b) 25 (c) 6 (d) 5
  6. 6.How far is the point (15, 8) from the origin (0, 0)? (a) 23 (b) 289 (c) 17 (d) 18
  7. 7.What is the distance between the points (3, 28) and (10, 4)? (a) 625 (b) 25 (c) 26 (d) 31
  8. 8.What is the midpoint of the line joining (5, 3) and (17, 1)? (a) (6, 1) (b) (11, 2) (c) (22, 4) (d) (2, 11)
  9. 9.What is the midpoint of the line joining (3, 5) and (7, 3)? (a) (5, 4) (b) (10, 8) (c) (2, 1) (d) (4, 5)
  10. 10.What is the midpoint of the line joining (4, 10) and (12, 12)? (a) (16, 22) (b) (8, 11) (c) (4, 1) (d) (11, 8)
  11. 11.How far is the point (6, 8) from the origin (0, 0)? (a) 14 (b) 10 (c) 11 (d) 100
  12. 12.In which quadrant does the point (−2, 9) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
  13. 13.What is the distance between the points (0, 7) and (7, 31)? (a) 625 (b) 31 (c) 26 (d) 25
  14. 14.What is the distance between the points (2, 1) and (17, 9)? (a) 18 (b) 17 (c) 289 (d) 23
  15. 15.In which quadrant does the point (9, −1) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  16. 16.What is the midpoint of the line joining (9, 4) and (11, 2)? (a) (3, 10) (b) (10, 3) (c) (20, 6) (d) (1, 1)
  17. 17.In which quadrant does the point (7, 4) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  18. 18.In which quadrant does the point (8, −7) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
  19. 19.What is the midpoint of the line joining (5, 3) and (7, 1)? (a) (12, 4) (b) (1, 1) (c) (6, 2) (d) (2, 6)
  20. 20.What is the distance between the points (6, 17) and (18, 1)? (a) 20 (b) 21 (c) 400 (d) 28
  21. 21.What is the midpoint of the line joining (1, 22) and (5, 10)? (a) (3, 16) (b) (6, 32) (c) (16, 3) (d) (2, 6)
  22. 22.What is the midpoint of the line joining (7, 8) and (19, 4)? (a) (13, 6) (b) (6, 13) (c) (26, 12) (d) (6, 2)
  23. 23.How far is the point (9, 12) from the origin (0, 0)? (a) 16 (b) 225 (c) 15 (d) 21
  24. 24.How far is the point (7, 24) from the origin (0, 0)? (a) 25 (b) 625 (c) 31 (d) 26
  25. 25.What is the distance between the points (5, 15) and (13, 0)? (a) 17 (b) 289 (c) 23 (d) 18
  26. 26.What is the distance between the points (1, 8) and (5, 5)? (a) 7 (b) 6 (c) 5 (d) 25
  27. 27.How far is the point (8, 6) from the origin (0, 0)? (a) 14 (b) 10 (c) 100 (d) 11
  28. 28.What is the distance between the points (9, 1) and (13, 4)? (a) 6 (b) 25 (c) 5 (d) 7
  29. 29.What is the midpoint of the line joining (4, 21) and (12, 9)? (a) (15, 8) (b) (16, 30) (c) (4, 6) (d) (8, 15)
  30. 30.What is the distance between the points (7, 3) and (19, 19)? (a) 21 (b) 28 (c) 400 (d) 20
  31. 31.What is the midpoint of the line joining (7, 20) and (19, 10)? (a) (15, 13) (b) (6, 5) (c) (26, 30) (d) (13, 15)
  32. 32.In which quadrant does the point (−5, −2) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  33. 33.How far is the point (24, 7) from the origin (0, 0)? (a) 31 (b) 25 (c) 26 (d) 625
  34. 34.What is the midpoint of the line joining (8, 0) and (16, 2)? (a) (4, 1) (b) (12, 1) (c) (1, 12) (d) (24, 2)
  35. 35.In which quadrant does the point (−3, 2) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  36. 36.What is the midpoint of the line joining (10, 12) and (18, 10)? (a) (28, 22) (b) (11, 14) (c) (14, 11) (d) (4, 1)
  37. 37.In which quadrant does the point (−2, −8) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  38. 38.In which quadrant does the point (−7, 8) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  39. 39.In which quadrant does the point (7, −2) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  40. 40.What is the distance between the points (0, 8) and (3, 12)? (a) 25 (b) 7 (c) 5 (d) 6

Answer key

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

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