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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 157 · 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 (2, 3) and (6, 13)? (a) (8, 4) (b) (2, 5) (c) (4, 8) (d) (8, 16)
  2. 2.In which quadrant does the point (−1, 7) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  3. 3.What is the midpoint of the line joining (2, 20) and (4, 10)? (a) (1, 5) (b) (3, 15) (c) (15, 3) (d) (6, 30)
  4. 4.How far is the point (15, 8) from the origin (0, 0)? (a) 289 (b) 17 (c) 18 (d) 23
  5. 5.In which quadrant does the point (2, 4) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  6. 6.In which quadrant does the point (−3, 8) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  7. 7.What is the distance between the points (7, 8) and (13, 16)? (a) 14 (b) 11 (c) 10 (d) 100
  8. 8.What is the distance between the points (3, 0) and (15, 5)? (a) 169 (b) 17 (c) 13 (d) 14
  9. 9.What is the distance between the points (9, 8) and (24, 0)? (a) 18 (b) 23 (c) 289 (d) 17
  10. 10.What is the distance between the points (1, 14) and (10, 2)? (a) 16 (b) 21 (c) 225 (d) 15
  11. 11.How far is the point (16, 12) from the origin (0, 0)? (a) 28 (b) 21 (c) 20 (d) 400
  12. 12.In which quadrant does the point (−1, 6) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  13. 13.What is the distance between the points (5, 5) and (8, 1)? (a) 6 (b) 25 (c) 5 (d) 7
  14. 14.What is the distance between the points (6, 20) and (14, 5)? (a) 23 (b) 18 (c) 289 (d) 17
  15. 15.What is the distance between the points (3, 7) and (6, 11)? (a) 6 (b) 25 (c) 7 (d) 5
  16. 16.In which quadrant does the point (−3, −3) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  17. 17.What is the distance between the points (6, 18) and (14, 3)? (a) 23 (b) 289 (c) 17 (d) 18
  18. 18.How far is the point (9, 12) from the origin (0, 0)? (a) 21 (b) 16 (c) 15 (d) 225
  19. 19.In which quadrant does the point (9, 2) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  20. 20.How far is the point (3, 4) from the origin (0, 0)? (a) 6 (b) 5 (c) 7 (d) 25
  21. 21.How far is the point (6, 8) from the origin (0, 0)? (a) 11 (b) 10 (c) 100 (d) 14
  22. 22.What is the distance between the points (1, 5) and (4, 9)? (a) 6 (b) 5 (c) 25 (d) 7
  23. 23.What is the distance between the points (6, 8) and (9, 12)? (a) 6 (b) 5 (c) 7 (d) 25
  24. 24.What is the distance between the points (3, 14) and (18, 6)? (a) 23 (b) 17 (c) 289 (d) 18
  25. 25.In which quadrant does the point (1, 6) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  26. 26.What is the distance between the points (8, 13) and (24, 1)? (a) 28 (b) 21 (c) 20 (d) 400
  27. 27.How far is the point (24, 7) from the origin (0, 0)? (a) 625 (b) 31 (c) 26 (d) 25
  28. 28.What is the midpoint of the line joining (8, 4) and (10, 6)? (a) (1, 1) (b) (9, 5) (c) (18, 10) (d) (5, 9)
  29. 29.What is the distance between the points (1, 21) and (9, 6)? (a) 289 (b) 18 (c) 17 (d) 23
  30. 30.What is the midpoint of the line joining (2, 4) and (8, 2)? (a) (3, 5) (b) (10, 6) (c) (3, 1) (d) (5, 3)
  31. 31.How far is the point (8, 15) from the origin (0, 0)? (a) 23 (b) 289 (c) 18 (d) 17
  32. 32.What is the distance between the points (3, 10) and (15, 5)? (a) 17 (b) 13 (c) 14 (d) 169
  33. 33.How far is the point (8, 6) from the origin (0, 0)? (a) 10 (b) 14 (c) 100 (d) 11
  34. 34.What is the midpoint of the line joining (10, 9) and (20, 21)? (a) (30, 30) (b) (16, 15) (c) (15, 15) (d) (5, 6)
  35. 35.What is the distance between the points (0, 16) and (16, 4)? (a) 21 (b) 400 (c) 28 (d) 20
  36. 36.In which quadrant does the point (9, −2) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  37. 37.What is the midpoint of the line joining (8, 3) and (12, 5)? (a) (20, 8) (b) (2, 1) (c) (4, 10) (d) (10, 4)
  38. 38.What is the distance between the points (6, 8) and (13, 32)? (a) 25 (b) 625 (c) 26 (d) 31
  39. 39.What is the midpoint of the line joining (10, 5) and (12, 17)? (a) (12, 11) (b) (1, 6) (c) (22, 22) (d) (11, 11)
  40. 40.What is the distance between the points (4, 1) and (16, 10)? (a) 21 (b) 225 (c) 16 (d) 15

Answer key

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

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