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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 86 · 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, 9) and (23, 21)? (a) 21 (b) 400 (c) 28 (d) 20
  2. 2.What is the distance between the points (2, 14) and (11, 2)? (a) 225 (b) 21 (c) 16 (d) 15
  3. 3.What is the distance between the points (9, 7) and (16, 31)? (a) 25 (b) 625 (c) 26 (d) 31
  4. 4.In which quadrant does the point (4, 6) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  5. 5.How far is the point (3, 4) from the origin (0, 0)? (a) 6 (b) 25 (c) 5 (d) 7
  6. 6.How far is the point (15, 8) from the origin (0, 0)? (a) 23 (b) 18 (c) 289 (d) 17
  7. 7.In which quadrant does the point (5, 1) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  8. 8.What is the distance between the points (2, 0) and (10, 15)? (a) 18 (b) 23 (c) 17 (d) 289
  9. 9.How far is the point (9, 12) from the origin (0, 0)? (a) 21 (b) 16 (c) 15 (d) 225
  10. 10.How far is the point (24, 7) from the origin (0, 0)? (a) 625 (b) 26 (c) 31 (d) 25
  11. 11.What is the midpoint of the line joining (6, 11) and (14, 9)? (a) (4, 1) (b) (10, 10) (c) (20, 20) (d) (11, 10)
  12. 12.In which quadrant does the point (−1, 9) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  13. 13.What is the midpoint of the line joining (6, 5) and (10, 9)? (a) (2, 2) (b) (7, 8) (c) (8, 7) (d) (16, 14)
  14. 14.What is the distance between the points (4, 1) and (8, 4)? (a) 6 (b) 25 (c) 5 (d) 7
  15. 15.What is the distance between the points (5, 4) and (29, 11)? (a) 625 (b) 31 (c) 26 (d) 25
  16. 16.What is the midpoint of the line joining (6, 7) and (14, 17)? (a) (20, 24) (b) (10, 12) (c) (4, 5) (d) (12, 10)
  17. 17.What is the distance between the points (3, 16) and (9, 8)? (a) 11 (b) 100 (c) 10 (d) 14
  18. 18.In which quadrant does the point (2, 1) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  19. 19.How far is the point (8, 6) from the origin (0, 0)? (a) 11 (b) 14 (c) 10 (d) 100
  20. 20.What is the midpoint of the line joining (4, 4) and (14, 8)? (a) (18, 12) (b) (9, 6) (c) (6, 9) (d) (5, 2)
  21. 21.How far is the point (4, 3) from the origin (0, 0)? (a) 7 (b) 25 (c) 6 (d) 5
  22. 22.What is the distance between the points (2, 5) and (9, 29)? (a) 31 (b) 25 (c) 625 (d) 26
  23. 23.What is the distance between the points (9, 27) and (16, 3)? (a) 31 (b) 625 (c) 26 (d) 25
  24. 24.In which quadrant does the point (−2, −2) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  25. 25.What is the distance between the points (7, 7) and (10, 3)? (a) 25 (b) 7 (c) 5 (d) 6
  26. 26.What is the distance between the points (5, 0) and (10, 12)? (a) 14 (b) 13 (c) 169 (d) 17
  27. 27.In which quadrant does the point (8, 9) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  28. 28.What is the midpoint of the line joining (6, 13) and (10, 5)? (a) (9, 8) (b) (8, 9) (c) (16, 18) (d) (2, 4)
  29. 29.In which quadrant does the point (−3, −7) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  30. 30.How far is the point (6, 8) from the origin (0, 0)? (a) 10 (b) 14 (c) 11 (d) 100
  31. 31.What is the midpoint of the line joining (4, 3) and (6, 9)? (a) (10, 12) (b) (1, 3) (c) (6, 5) (d) (5, 6)
  32. 32.What is the distance between the points (1, 31) and (8, 7)? (a) 26 (b) 25 (c) 625 (d) 31
  33. 33.What is the distance between the points (2, 3) and (18, 15)? (a) 28 (b) 21 (c) 400 (d) 20
  34. 34.What is the midpoint of the line joining (9, 7) and (11, 9)? (a) (20, 16) (b) (10, 8) (c) (1, 1) (d) (8, 10)
  35. 35.What is the distance between the points (0, 1) and (8, 16)? (a) 17 (b) 23 (c) 18 (d) 289
  36. 36.How far is the point (12, 16) from the origin (0, 0)? (a) 20 (b) 28 (c) 21 (d) 400
  37. 37.How far is the point (16, 12) from the origin (0, 0)? (a) 20 (b) 21 (c) 28 (d) 400
  38. 38.How far is the point (12, 9) from the origin (0, 0)? (a) 225 (b) 16 (c) 21 (d) 15
  39. 39.What is the midpoint of the line joining (6, 7) and (14, 15)? (a) (11, 10) (b) (20, 22) (c) (10, 11) (d) (4, 4)
  40. 40.In which quadrant does the point (−1, −6) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant

Answer key

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

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