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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 231 · 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 (6, 8) from the origin (0, 0)? (a) 11 (b) 100 (c) 14 (d) 10
  2. 2.In which quadrant does the point (4, 2) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  3. 3.How far is the point (16, 12) from the origin (0, 0)? (a) 28 (b) 21 (c) 20 (d) 400
  4. 4.In which quadrant does the point (3, 8) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  5. 5.In which quadrant does the point (4, −5) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  6. 6.In which quadrant does the point (3, 1) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  7. 7.In which quadrant does the point (2, −8) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  8. 8.What is the midpoint of the line joining (7, 8) and (19, 12)? (a) (13, 10) (b) (6, 2) (c) (26, 20) (d) (10, 13)
  9. 9.What is the midpoint of the line joining (10, 4) and (22, 8)? (a) (6, 16) (b) (32, 12) (c) (16, 6) (d) (6, 2)
  10. 10.What is the distance between the points (1, 21) and (13, 5)? (a) 20 (b) 28 (c) 21 (d) 400
  11. 11.What is the midpoint of the line joining (0, 1) and (2, 5)? (a) (3, 1) (b) (1, 2) (c) (2, 6) (d) (1, 3)
  12. 12.What is the midpoint of the line joining (8, 9) and (16, 3)? (a) (24, 12) (b) (4, 3) (c) (6, 12) (d) (12, 6)
  13. 13.How far is the point (12, 9) from the origin (0, 0)? (a) 21 (b) 225 (c) 15 (d) 16
  14. 14.What is the midpoint of the line joining (2, 5) and (14, 1)? (a) (8, 3) (b) (3, 8) (c) (16, 6) (d) (6, 2)
  15. 15.In which quadrant does the point (−9, 4) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  16. 16.What is the distance between the points (6, 10) and (9, 6)? (a) 6 (b) 5 (c) 25 (d) 7
  17. 17.What is the distance between the points (9, 9) and (15, 17)? (a) 14 (b) 100 (c) 11 (d) 10
  18. 18.What is the midpoint of the line joining (5, 5) and (13, 3)? (a) (9, 4) (b) (4, 1) (c) (18, 8) (d) (4, 9)
  19. 19.In which quadrant does the point (6, 5) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  20. 20.What is the distance between the points (0, 6) and (15, 14)? (a) 17 (b) 18 (c) 23 (d) 289
  21. 21.What is the distance between the points (9, 0) and (25, 12)? (a) 21 (b) 28 (c) 400 (d) 20
  22. 22.In which quadrant does the point (−8, −6) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  23. 23.In which quadrant does the point (−8, 6) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  24. 24.What is the distance between the points (6, 9) and (30, 16)? (a) 26 (b) 25 (c) 625 (d) 31
  25. 25.What is the distance between the points (0, 9) and (3, 5)? (a) 6 (b) 7 (c) 5 (d) 25
  26. 26.What is the distance between the points (1, 9) and (13, 4)? (a) 169 (b) 14 (c) 13 (d) 17
  27. 27.What is the distance between the points (8, 4) and (15, 28)? (a) 31 (b) 625 (c) 26 (d) 25
  28. 28.What is the midpoint of the line joining (5, 8) and (7, 20)? (a) (12, 28) (b) (6, 14) (c) (14, 6) (d) (1, 6)
  29. 29.What is the distance between the points (4, 9) and (12, 15)? (a) 10 (b) 100 (c) 14 (d) 11
  30. 30.What is the midpoint of the line joining (2, 14) and (10, 6)? (a) (6, 10) (b) (12, 20) (c) (4, 4) (d) (10, 6)
  31. 31.How far is the point (8, 6) from the origin (0, 0)? (a) 11 (b) 100 (c) 14 (d) 10
  32. 32.How far is the point (5, 12) from the origin (0, 0)? (a) 14 (b) 169 (c) 13 (d) 17
  33. 33.What is the distance between the points (1, 6) and (4, 2)? (a) 5 (b) 25 (c) 6 (d) 7
  34. 34.What is the midpoint of the line joining (4, 3) and (6, 15)? (a) (10, 18) (b) (5, 9) (c) (1, 6) (d) (9, 5)
  35. 35.What is the midpoint of the line joining (5, 6) and (15, 4)? (a) (5, 1) (b) (10, 5) (c) (5, 10) (d) (20, 10)
  36. 36.What is the distance between the points (3, 0) and (18, 8)? (a) 18 (b) 289 (c) 23 (d) 17
  37. 37.How far is the point (15, 8) from the origin (0, 0)? (a) 23 (b) 17 (c) 18 (d) 289
  38. 38.In which quadrant does the point (6, 1) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  39. 39.What is the midpoint of the line joining (4, 1) and (8, 5)? (a) (3, 6) (b) (12, 6) (c) (2, 2) (d) (6, 3)
  40. 40.How far is the point (9, 12) from the origin (0, 0)? (a) 15 (b) 225 (c) 21 (d) 16

Answer key

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

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