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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 202 · 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 (6, 9) and (18, 3)? (a) (12, 6) (b) (6, 3) (c) (24, 12) (d) (6, 12)
  2. 2.In which quadrant does the point (−4, 6) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  3. 3.In which quadrant does the point (7, −6) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  4. 4.How far is the point (7, 24) from the origin (0, 0)? (a) 25 (b) 31 (c) 625 (d) 26
  5. 5.What is the distance between the points (9, 16) and (18, 4)? (a) 16 (b) 225 (c) 21 (d) 15
  6. 6.What is the distance between the points (5, 0) and (11, 8)? (a) 100 (b) 14 (c) 11 (d) 10
  7. 7.In which quadrant does the point (4, 5) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  8. 8.How far is the point (3, 4) from the origin (0, 0)? (a) 7 (b) 5 (c) 6 (d) 25
  9. 9.How far is the point (6, 8) from the origin (0, 0)? (a) 14 (b) 10 (c) 11 (d) 100
  10. 10.What is the distance between the points (3, 14) and (11, 8)? (a) 14 (b) 100 (c) 11 (d) 10
  11. 11.What is the midpoint of the line joining (0, 3) and (12, 13)? (a) (8, 6) (b) (6, 5) (c) (12, 16) (d) (6, 8)
  12. 12.What is the distance between the points (1, 9) and (7, 1)? (a) 10 (b) 100 (c) 14 (d) 11
  13. 13.What is the midpoint of the line joining (1, 8) and (3, 0)? (a) (4, 2) (b) (4, 8) (c) (2, 4) (d) (1, 4)
  14. 14.What is the distance between the points (4, 5) and (12, 20)? (a) 289 (b) 17 (c) 18 (d) 23
  15. 15.What is the distance between the points (0, 6) and (8, 21)? (a) 23 (b) 18 (c) 17 (d) 289
  16. 16.What is the distance between the points (5, 24) and (12, 0)? (a) 26 (b) 31 (c) 25 (d) 625
  17. 17.What is the midpoint of the line joining (8, 8) and (20, 0)? (a) (14, 4) (b) (28, 8) (c) (4, 14) (d) (6, 4)
  18. 18.In which quadrant does the point (6, 6) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  19. 19.What is the midpoint of the line joining (3, 12) and (11, 8)? (a) (7, 10) (b) (4, 2) (c) (10, 7) (d) (14, 20)
  20. 20.How far is the point (24, 7) from the origin (0, 0)? (a) 625 (b) 25 (c) 31 (d) 26
  21. 21.In which quadrant does the point (7, 1) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  22. 22.In which quadrant does the point (4, 4) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  23. 23.In which quadrant does the point (−8, 8) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  24. 24.In which quadrant does the point (4, 2) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  25. 25.What is the midpoint of the line joining (9, 12) and (17, 6)? (a) (9, 13) (b) (26, 18) (c) (13, 9) (d) (4, 3)
  26. 26.What is the distance between the points (1, 4) and (6, 16)? (a) 13 (b) 169 (c) 17 (d) 14
  27. 27.How far is the point (16, 12) from the origin (0, 0)? (a) 28 (b) 21 (c) 400 (d) 20
  28. 28.What is the midpoint of the line joining (1, 6) and (9, 0)? (a) (4, 3) (b) (3, 5) (c) (10, 6) (d) (5, 3)
  29. 29.What is the midpoint of the line joining (4, 4) and (14, 16)? (a) (10, 9) (b) (9, 10) (c) (5, 6) (d) (18, 20)
  30. 30.What is the midpoint of the line joining (2, 2) and (6, 4)? (a) (2, 1) (b) (4, 3) (c) (8, 6) (d) (3, 4)
  31. 31.How far is the point (12, 9) from the origin (0, 0)? (a) 225 (b) 16 (c) 15 (d) 21
  32. 32.What is the distance between the points (0, 14) and (9, 2)? (a) 15 (b) 16 (c) 225 (d) 21
  33. 33.What is the midpoint of the line joining (5, 10) and (9, 14)? (a) (2, 2) (b) (12, 7) (c) (14, 24) (d) (7, 12)
  34. 34.What is the midpoint of the line joining (0, 8) and (2, 12)? (a) (10, 1) (b) (1, 10) (c) (1, 2) (d) (2, 20)
  35. 35.What is the midpoint of the line joining (2, 7) and (8, 15)? (a) (10, 22) (b) (3, 4) (c) (11, 5) (d) (5, 11)
  36. 36.What is the midpoint of the line joining (0, 2) and (6, 8)? (a) (6, 10) (b) (5, 3) (c) (3, 5) (d) (3, 3)
  37. 37.In which quadrant does the point (−7, −6) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  38. 38.What is the distance between the points (7, 15) and (23, 3)? (a) 400 (b) 21 (c) 28 (d) 20
  39. 39.What is the distance between the points (5, 22) and (17, 6)? (a) 21 (b) 400 (c) 20 (d) 28
  40. 40.What is the midpoint of the line joining (6, 16) and (16, 10)? (a) (13, 11) (b) (11, 13) (c) (22, 26) (d) (5, 3)

Answer key

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

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