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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 712 · 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 distance between the points (7, 6) and (15, 0)? (a) 10 (b) 100 (c) 11 (d) 14
  2. 2.What is the midpoint of the line joining (2, 0) and (4, 4)? (a) (1, 2) (b) (6, 4) (c) (2, 3) (d) (3, 2)
  3. 3.What is the midpoint of the line joining (10, 10) and (14, 14)? (a) (24, 24) (b) (2, 2) (c) (12, 12) (d) (13, 12)
  4. 4.What is the midpoint of the line joining (7, 0) and (11, 12)? (a) (2, 6) (b) (18, 12) (c) (9, 6) (d) (6, 9)
  5. 5.What is the distance between the points (0, 2) and (6, 10)? (a) 100 (b) 10 (c) 14 (d) 11
  6. 6.In which quadrant does the point (9, −6) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  7. 7.What is the distance between the points (1, 7) and (5, 10)? (a) 7 (b) 6 (c) 5 (d) 25
  8. 8.How far is the point (12, 9) from the origin (0, 0)? (a) 16 (b) 225 (c) 21 (d) 15
  9. 9.How far is the point (3, 4) from the origin (0, 0)? (a) 6 (b) 5 (c) 7 (d) 25
  10. 10.How far is the point (5, 12) from the origin (0, 0)? (a) 14 (b) 17 (c) 13 (d) 169
  11. 11.What is the distance between the points (1, 0) and (8, 24)? (a) 26 (b) 625 (c) 25 (d) 31
  12. 12.In which quadrant does the point (−6, −5) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  13. 13.In which quadrant does the point (2, 1) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  14. 14.What is the distance between the points (5, 8) and (8, 12)? (a) 5 (b) 25 (c) 6 (d) 7
  15. 15.In which quadrant does the point (−3, −2) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  16. 16.In which quadrant does the point (−8, −7) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  17. 17.In which quadrant does the point (−8, 3) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
  18. 18.What is the distance between the points (3, 9) and (15, 0)? (a) 16 (b) 15 (c) 225 (d) 21
  19. 19.In which quadrant does the point (4, −1) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  20. 20.What is the distance between the points (3, 6) and (18, 14)? (a) 18 (b) 289 (c) 17 (d) 23
  21. 21.What is the distance between the points (9, 9) and (13, 6)? (a) 25 (b) 5 (c) 6 (d) 7
  22. 22.What is the distance between the points (1, 8) and (7, 16)? (a) 14 (b) 100 (c) 10 (d) 11
  23. 23.What is the distance between the points (4, 22) and (16, 6)? (a) 21 (b) 28 (c) 400 (d) 20
  24. 24.How far is the point (24, 7) from the origin (0, 0)? (a) 31 (b) 25 (c) 26 (d) 625
  25. 25.What is the distance between the points (3, 14) and (15, 9)? (a) 17 (b) 169 (c) 14 (d) 13
  26. 26.What is the distance between the points (7, 6) and (11, 9)? (a) 7 (b) 5 (c) 25 (d) 6
  27. 27.What is the distance between the points (8, 0) and (12, 3)? (a) 25 (b) 6 (c) 7 (d) 5
  28. 28.What is the distance between the points (1, 5) and (6, 17)? (a) 14 (b) 169 (c) 17 (d) 13
  29. 29.In which quadrant does the point (−6, −1) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  30. 30.What is the distance between the points (8, 14) and (24, 2)? (a) 21 (b) 400 (c) 28 (d) 20
  31. 31.What is the distance between the points (3, 2) and (11, 17)? (a) 17 (b) 18 (c) 289 (d) 23
  32. 32.How far is the point (7, 24) from the origin (0, 0)? (a) 25 (b) 31 (c) 26 (d) 625
  33. 33.What is the midpoint of the line joining (5, 9) and (15, 21)? (a) (15, 10) (b) (20, 30) (c) (10, 15) (d) (5, 6)
  34. 34.What is the distance between the points (2, 16) and (8, 8)? (a) 10 (b) 14 (c) 11 (d) 100
  35. 35.What is the midpoint of the line joining (3, 7) and (15, 15)? (a) (6, 4) (b) (11, 9) (c) (18, 22) (d) (9, 11)
  36. 36.What is the distance between the points (0, 2) and (9, 14)? (a) 16 (b) 225 (c) 15 (d) 21
  37. 37.In which quadrant does the point (−1, 5) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  38. 38.What is the distance between the points (3, 6) and (27, 13)? (a) 625 (b) 31 (c) 26 (d) 25
  39. 39.What is the midpoint of the line joining (3, 4) and (13, 0)? (a) (8, 2) (b) (16, 4) (c) (5, 2) (d) (2, 8)
  40. 40.What is the midpoint of the line joining (4, 1) and (14, 11)? (a) (18, 12) (b) (9, 6) (c) (6, 9) (d) (5, 5)

Answer key

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

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