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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 829 · 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 (1, −2) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  2. 2.What is the distance between the points (5, 21) and (10, 9)? (a) 13 (b) 169 (c) 14 (d) 17
  3. 3.How far is the point (24, 7) from the origin (0, 0)? (a) 25 (b) 26 (c) 31 (d) 625
  4. 4.What is the midpoint of the line joining (1, 10) and (7, 6)? (a) (3, 2) (b) (4, 8) (c) (8, 16) (d) (8, 4)
  5. 5.What is the midpoint of the line joining (10, 12) and (12, 8)? (a) (1, 2) (b) (11, 10) (c) (10, 11) (d) (22, 20)
  6. 6.In which quadrant does the point (−6, 5) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  7. 7.How far is the point (9, 12) from the origin (0, 0)? (a) 15 (b) 225 (c) 21 (d) 16
  8. 8.What is the midpoint of the line joining (2, 10) and (8, 22)? (a) (16, 5) (b) (5, 16) (c) (10, 32) (d) (3, 6)
  9. 9.What is the midpoint of the line joining (1, 2) and (5, 10)? (a) (6, 12) (b) (2, 4) (c) (3, 6) (d) (6, 3)
  10. 10.How far is the point (16, 12) from the origin (0, 0)? (a) 400 (b) 28 (c) 20 (d) 21
  11. 11.What is the midpoint of the line joining (8, 11) and (20, 5)? (a) (6, 3) (b) (14, 8) (c) (8, 14) (d) (28, 16)
  12. 12.What is the midpoint of the line joining (0, 13) and (4, 1)? (a) (2, 7) (b) (7, 2) (c) (2, 6) (d) (4, 14)
  13. 13.What is the midpoint of the line joining (2, 14) and (12, 2)? (a) (5, 6) (b) (7, 8) (c) (14, 16) (d) (8, 7)
  14. 14.How far is the point (8, 15) from the origin (0, 0)? (a) 18 (b) 17 (c) 289 (d) 23
  15. 15.In which quadrant does the point (−7, 8) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  16. 16.How far is the point (5, 12) from the origin (0, 0)? (a) 13 (b) 14 (c) 17 (d) 169
  17. 17.How far is the point (4, 3) from the origin (0, 0)? (a) 6 (b) 25 (c) 7 (d) 5
  18. 18.What is the midpoint of the line joining (5, 0) and (9, 6)? (a) (2, 3) (b) (3, 7) (c) (7, 3) (d) (14, 6)
  19. 19.How far is the point (8, 6) from the origin (0, 0)? (a) 14 (b) 11 (c) 10 (d) 100
  20. 20.In which quadrant does the point (2, 3) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  21. 21.What is the distance between the points (2, 18) and (14, 9)? (a) 21 (b) 15 (c) 225 (d) 16
  22. 22.What is the distance between the points (9, 21) and (21, 5)? (a) 20 (b) 28 (c) 400 (d) 21
  23. 23.What is the midpoint of the line joining (5, 6) and (17, 10)? (a) (8, 11) (b) (22, 16) (c) (11, 8) (d) (6, 2)
  24. 24.What is the distance between the points (5, 0) and (21, 12)? (a) 28 (b) 20 (c) 21 (d) 400
  25. 25.In which quadrant does the point (−3, 1) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  26. 26.In which quadrant does the point (6, −2) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  27. 27.What is the distance between the points (6, 6) and (10, 9)? (a) 7 (b) 5 (c) 6 (d) 25
  28. 28.What is the distance between the points (3, 8) and (10, 32)? (a) 26 (b) 625 (c) 31 (d) 25
  29. 29.What is the distance between the points (3, 7) and (15, 12)? (a) 14 (b) 13 (c) 169 (d) 17
  30. 30.What is the midpoint of the line joining (6, 4) and (18, 16)? (a) (6, 6) (b) (12, 10) (c) (24, 20) (d) (10, 12)
  31. 31.What is the midpoint of the line joining (8, 2) and (14, 6)? (a) (4, 11) (b) (22, 8) (c) (11, 4) (d) (3, 2)
  32. 32.What is the midpoint of the line joining (7, 3) and (11, 11)? (a) (18, 14) (b) (9, 7) (c) (7, 9) (d) (2, 4)
  33. 33.What is the midpoint of the line joining (0, 3) and (8, 1)? (a) (2, 4) (b) (4, 1) (c) (4, 2) (d) (8, 4)
  34. 34.In which quadrant does the point (−8, −2) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  35. 35.What is the midpoint of the line joining (7, 8) and (19, 12)? (a) (13, 10) (b) (6, 2) (c) (10, 13) (d) (26, 20)
  36. 36.In which quadrant does the point (−2, −4) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  37. 37.What is the distance between the points (0, 9) and (12, 18)? (a) 15 (b) 16 (c) 21 (d) 225
  38. 38.What is the midpoint of the line joining (6, 10) and (8, 6)? (a) (7, 8) (b) (8, 7) (c) (14, 16) (d) (1, 2)
  39. 39.In which quadrant does the point (−9, −4) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  40. 40.What is the distance between the points (9, 24) and (16, 0)? (a) 26 (b) 625 (c) 31 (d) 25

Answer key

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

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