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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 111 · 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.In which quadrant does the point (6, −7) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  2. 2.What is the distance between the points (7, 9) and (19, 25)? (a) 400 (b) 28 (c) 21 (d) 20
  3. 3.How far is the point (9, 12) from the origin (0, 0)? (a) 16 (b) 225 (c) 21 (d) 15
  4. 4.What is the distance between the points (6, 6) and (14, 0)? (a) 11 (b) 14 (c) 100 (d) 10
  5. 5.What is the distance between the points (3, 14) and (18, 6)? (a) 17 (b) 289 (c) 23 (d) 18
  6. 6.What is the midpoint of the line joining (10, 8) and (14, 10)? (a) (2, 1) (b) (12, 9) (c) (24, 18) (d) (9, 12)
  7. 7.In which quadrant does the point (−7, −4) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  8. 8.In which quadrant does the point (−9, 1) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  9. 9.What is the midpoint of the line joining (7, 6) and (15, 4)? (a) (22, 10) (b) (5, 11) (c) (11, 5) (d) (4, 1)
  10. 10.In which quadrant does the point (3, 2) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  11. 11.What is the midpoint of the line joining (1, 13) and (5, 5)? (a) (6, 18) (b) (9, 3) (c) (3, 9) (d) (2, 4)
  12. 12.How far is the point (3, 4) from the origin (0, 0)? (a) 25 (b) 6 (c) 7 (d) 5
  13. 13.What is the distance between the points (6, 8) and (12, 0)? (a) 10 (b) 14 (c) 100 (d) 11
  14. 14.How far is the point (12, 16) from the origin (0, 0)? (a) 28 (b) 400 (c) 20 (d) 21
  15. 15.What is the midpoint of the line joining (6, 3) and (8, 5)? (a) (4, 7) (b) (7, 4) (c) (1, 1) (d) (14, 8)
  16. 16.How far is the point (6, 8) from the origin (0, 0)? (a) 14 (b) 100 (c) 11 (d) 10
  17. 17.In which quadrant does the point (5, 1) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  18. 18.What is the distance between the points (8, 13) and (11, 9)? (a) 5 (b) 7 (c) 25 (d) 6
  19. 19.What is the distance between the points (3, 19) and (19, 7)? (a) 20 (b) 28 (c) 21 (d) 400
  20. 20.What is the midpoint of the line joining (9, 8) and (13, 0)? (a) (22, 8) (b) (11, 4) (c) (4, 11) (d) (2, 4)
  21. 21.What is the distance between the points (0, 3) and (12, 12)? (a) 225 (b) 21 (c) 15 (d) 16
  22. 22.What is the distance between the points (1, 18) and (13, 2)? (a) 20 (b) 400 (c) 21 (d) 28
  23. 23.How far is the point (8, 6) from the origin (0, 0)? (a) 100 (b) 11 (c) 10 (d) 14
  24. 24.What is the distance between the points (5, 12) and (20, 4)? (a) 18 (b) 17 (c) 23 (d) 289
  25. 25.What is the distance between the points (3, 7) and (15, 2)? (a) 14 (b) 169 (c) 17 (d) 13
  26. 26.In which quadrant does the point (−1, 6) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  27. 27.What is the distance between the points (1, 5) and (25, 12)? (a) 25 (b) 26 (c) 625 (d) 31
  28. 28.How far is the point (12, 9) from the origin (0, 0)? (a) 21 (b) 225 (c) 16 (d) 15
  29. 29.What is the distance between the points (7, 4) and (16, 16)? (a) 21 (b) 16 (c) 15 (d) 225
  30. 30.What is the midpoint of the line joining (2, 18) and (8, 6)? (a) (10, 24) (b) (3, 6) (c) (12, 5) (d) (5, 12)
  31. 31.In which quadrant does the point (1, 9) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
  32. 32.What is the distance between the points (0, 4) and (8, 10)? (a) 11 (b) 10 (c) 14 (d) 100
  33. 33.What is the midpoint of the line joining (10, 5) and (12, 15)? (a) (11, 10) (b) (22, 20) (c) (1, 5) (d) (10, 11)
  34. 34.How far is the point (12, 5) from the origin (0, 0)? (a) 13 (b) 17 (c) 169 (d) 14
  35. 35.In which quadrant does the point (−3, 4) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  36. 36.What is the distance between the points (1, 9) and (13, 25)? (a) 28 (b) 21 (c) 20 (d) 400
  37. 37.In which quadrant does the point (−9, 9) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  38. 38.What is the distance between the points (9, 1) and (15, 9)? (a) 14 (b) 100 (c) 11 (d) 10
  39. 39.In which quadrant does the point (−6, 3) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  40. 40.What is the midpoint of the line joining (8, 7) and (18, 13)? (a) (13, 10) (b) (5, 3) (c) (10, 13) (d) (26, 20)

Answer key

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

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