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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 544 · 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, 3) and (23, 15)? (a) 28 (b) 400 (c) 21 (d) 20
  2. 2.In which quadrant does the point (9, −9) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  3. 3.How far is the point (9, 12) from the origin (0, 0)? (a) 225 (b) 16 (c) 21 (d) 15
  4. 4.What is the midpoint of the line joining (10, 13) and (16, 5)? (a) (9, 13) (b) (26, 18) (c) (3, 4) (d) (13, 9)
  5. 5.What is the distance between the points (1, 8) and (7, 0)? (a) 100 (b) 11 (c) 14 (d) 10
  6. 6.What is the midpoint of the line joining (3, 13) and (5, 9)? (a) (8, 22) (b) (11, 4) (c) (1, 2) (d) (4, 11)
  7. 7.In which quadrant does the point (−2, −3) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  8. 8.In which quadrant does the point (−5, −6) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  9. 9.What is the distance between the points (0, 12) and (5, 0)? (a) 13 (b) 169 (c) 17 (d) 14
  10. 10.What is the midpoint of the line joining (10, 2) and (20, 10)? (a) (6, 15) (b) (30, 12) (c) (5, 4) (d) (15, 6)
  11. 11.In which quadrant does the point (2, 5) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  12. 12.What is the midpoint of the line joining (0, 4) and (2, 12)? (a) (2, 16) (b) (1, 8) (c) (8, 1) (d) (1, 4)
  13. 13.How far is the point (16, 12) from the origin (0, 0)? (a) 21 (b) 20 (c) 400 (d) 28
  14. 14.How far is the point (12, 5) from the origin (0, 0)? (a) 14 (b) 13 (c) 169 (d) 17
  15. 15.What is the distance between the points (3, 7) and (11, 13)? (a) 11 (b) 10 (c) 14 (d) 100
  16. 16.In which quadrant does the point (1, 7) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  17. 17.What is the distance between the points (7, 8) and (31, 1)? (a) 26 (b) 625 (c) 25 (d) 31
  18. 18.What is the distance between the points (4, 6) and (8, 9)? (a) 25 (b) 6 (c) 7 (d) 5
  19. 19.What is the distance between the points (1, 9) and (8, 33)? (a) 26 (b) 25 (c) 625 (d) 31
  20. 20.In which quadrant does the point (−5, −8) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  21. 21.What is the midpoint of the line joining (9, 0) and (11, 4)? (a) (1, 2) (b) (2, 10) (c) (10, 2) (d) (20, 4)
  22. 22.What is the distance between the points (9, 15) and (14, 3)? (a) 169 (b) 17 (c) 13 (d) 14
  23. 23.What is the midpoint of the line joining (3, 18) and (15, 6)? (a) (6, 6) (b) (9, 12) (c) (18, 24) (d) (12, 9)
  24. 24.What is the distance between the points (7, 1) and (15, 7)? (a) 11 (b) 100 (c) 14 (d) 10
  25. 25.In which quadrant does the point (−1, 5) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  26. 26.How far is the point (12, 9) from the origin (0, 0)? (a) 21 (b) 16 (c) 15 (d) 225
  27. 27.What is the midpoint of the line joining (9, 1) and (21, 5)? (a) (6, 2) (b) (30, 6) (c) (3, 15) (d) (15, 3)
  28. 28.How far is the point (4, 3) from the origin (0, 0)? (a) 6 (b) 7 (c) 5 (d) 25
  29. 29.What is the distance between the points (1, 7) and (9, 22)? (a) 289 (b) 23 (c) 17 (d) 18
  30. 30.What is the midpoint of the line joining (8, 3) and (18, 5)? (a) (26, 8) (b) (4, 13) (c) (5, 1) (d) (13, 4)
  31. 31.How far is the point (8, 6) from the origin (0, 0)? (a) 11 (b) 10 (c) 14 (d) 100
  32. 32.In which quadrant does the point (−4, 1) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  33. 33.What is the distance between the points (9, 2) and (13, 5)? (a) 7 (b) 6 (c) 25 (d) 5
  34. 34.What is the distance between the points (7, 1) and (19, 17)? (a) 21 (b) 28 (c) 20 (d) 400
  35. 35.What is the midpoint of the line joining (8, 16) and (16, 10)? (a) (4, 3) (b) (13, 12) (c) (24, 26) (d) (12, 13)
  36. 36.How far is the point (12, 16) from the origin (0, 0)? (a) 28 (b) 21 (c) 400 (d) 20
  37. 37.What is the distance between the points (4, 5) and (20, 17)? (a) 28 (b) 400 (c) 21 (d) 20
  38. 38.In which quadrant does the point (7, −1) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  39. 39.What is the midpoint of the line joining (5, 1) and (11, 9)? (a) (16, 10) (b) (8, 5) (c) (5, 8) (d) (3, 4)
  40. 40.In which quadrant does the point (−5, −1) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant

Answer key

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

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