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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 447 · 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 (5, 4) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  2. 2.What is the midpoint of the line joining (2, 15) and (12, 5)? (a) (14, 20) (b) (7, 10) (c) (10, 7) (d) (5, 5)
  3. 3.What is the midpoint of the line joining (3, 8) and (11, 6)? (a) (4, 1) (b) (8, 7) (c) (7, 7) (d) (14, 14)
  4. 4.How far is the point (3, 4) from the origin (0, 0)? (a) 6 (b) 7 (c) 25 (d) 5
  5. 5.How far is the point (24, 7) from the origin (0, 0)? (a) 31 (b) 25 (c) 625 (d) 26
  6. 6.In which quadrant does the point (−5, −9) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  7. 7.What is the midpoint of the line joining (6, 2) and (12, 10)? (a) (9, 6) (b) (18, 12) (c) (6, 9) (d) (3, 4)
  8. 8.In which quadrant does the point (−8, 9) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  9. 9.In which quadrant does the point (−2, 6) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  10. 10.What is the distance between the points (2, 9) and (26, 16)? (a) 625 (b) 31 (c) 25 (d) 26
  11. 11.What is the midpoint of the line joining (4, 10) and (8, 18)? (a) (14, 6) (b) (12, 28) (c) (2, 4) (d) (6, 14)
  12. 12.What is the midpoint of the line joining (0, 12) and (2, 6)? (a) (1, 3) (b) (1, 9) (c) (2, 18) (d) (9, 1)
  13. 13.How far is the point (8, 15) from the origin (0, 0)? (a) 17 (b) 23 (c) 289 (d) 18
  14. 14.What is the distance between the points (7, 6) and (10, 10)? (a) 6 (b) 25 (c) 5 (d) 7
  15. 15.What is the distance between the points (4, 7) and (16, 23)? (a) 20 (b) 28 (c) 400 (d) 21
  16. 16.How far is the point (5, 12) from the origin (0, 0)? (a) 13 (b) 17 (c) 14 (d) 169
  17. 17.What is the distance between the points (7, 5) and (19, 21)? (a) 28 (b) 21 (c) 20 (d) 400
  18. 18.What is the midpoint of the line joining (2, 5) and (12, 3)? (a) (14, 8) (b) (4, 7) (c) (7, 4) (d) (5, 1)
  19. 19.How far is the point (12, 9) from the origin (0, 0)? (a) 225 (b) 16 (c) 21 (d) 15
  20. 20.What is the distance between the points (5, 17) and (17, 8)? (a) 16 (b) 15 (c) 21 (d) 225
  21. 21.What is the midpoint of the line joining (2, 13) and (14, 3)? (a) (8, 8) (b) (6, 5) (c) (16, 16) (d) (9, 8)
  22. 22.How far is the point (4, 3) from the origin (0, 0)? (a) 7 (b) 25 (c) 6 (d) 5
  23. 23.What is the midpoint of the line joining (0, 14) and (2, 10)? (a) (12, 1) (b) (2, 24) (c) (1, 12) (d) (1, 2)
  24. 24.What is the midpoint of the line joining (5, 8) and (9, 16)? (a) (7, 12) (b) (14, 24) (c) (12, 7) (d) (2, 4)
  25. 25.What is the midpoint of the line joining (9, 7) and (19, 19)? (a) (14, 13) (b) (13, 14) (c) (28, 26) (d) (5, 6)
  26. 26.What is the midpoint of the line joining (1, 15) and (13, 9)? (a) (14, 24) (b) (12, 7) (c) (6, 3) (d) (7, 12)
  27. 27.How far is the point (15, 8) from the origin (0, 0)? (a) 17 (b) 289 (c) 18 (d) 23
  28. 28.What is the distance between the points (8, 11) and (14, 3)? (a) 100 (b) 14 (c) 10 (d) 11
  29. 29.In which quadrant does the point (−5, −7) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  30. 30.In which quadrant does the point (−2, 9) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
  31. 31.What is the distance between the points (1, 7) and (4, 11)? (a) 5 (b) 7 (c) 6 (d) 25
  32. 32.In which quadrant does the point (−8, 2) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  33. 33.What is the distance between the points (1, 19) and (10, 7)? (a) 21 (b) 15 (c) 16 (d) 225
  34. 34.What is the distance between the points (2, 5) and (14, 21)? (a) 28 (b) 20 (c) 400 (d) 21
  35. 35.What is the midpoint of the line joining (6, 6) and (18, 12)? (a) (6, 3) (b) (9, 12) (c) (24, 18) (d) (12, 9)
  36. 36.What is the midpoint of the line joining (1, 9) and (3, 15)? (a) (4, 24) (b) (12, 2) (c) (1, 3) (d) (2, 12)
  37. 37.How far is the point (6, 8) from the origin (0, 0)? (a) 14 (b) 11 (c) 100 (d) 10
  38. 38.What is the distance between the points (2, 13) and (5, 9)? (a) 25 (b) 6 (c) 7 (d) 5
  39. 39.In which quadrant does the point (6, 5) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  40. 40.What is the midpoint of the line joining (1, 16) and (5, 6)? (a) (11, 3) (b) (6, 22) (c) (2, 5) (d) (3, 11)

Answer key

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

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