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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 293 · 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 (−8, 7) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  2. 2.What is the distance between the points (5, 4) and (14, 16)? (a) 16 (b) 225 (c) 15 (d) 21
  3. 3.What is the midpoint of the line joining (10, 0) and (22, 6)? (a) (16, 3) (b) (32, 6) (c) (3, 16) (d) (6, 3)
  4. 4.What is the midpoint of the line joining (3, 15) and (7, 7)? (a) (11, 5) (b) (10, 22) (c) (2, 4) (d) (5, 11)
  5. 5.What is the midpoint of the line joining (1, 4) and (5, 8)? (a) (3, 6) (b) (2, 2) (c) (6, 12) (d) (6, 3)
  6. 6.What is the distance between the points (5, 8) and (13, 23)? (a) 289 (b) 23 (c) 18 (d) 17
  7. 7.What is the distance between the points (7, 29) and (14, 5)? (a) 26 (b) 25 (c) 31 (d) 625
  8. 8.How far is the point (15, 8) from the origin (0, 0)? (a) 18 (b) 289 (c) 17 (d) 23
  9. 9.How far is the point (3, 4) from the origin (0, 0)? (a) 5 (b) 25 (c) 6 (d) 7
  10. 10.How far is the point (12, 5) from the origin (0, 0)? (a) 17 (b) 14 (c) 169 (d) 13
  11. 11.What is the distance between the points (0, 0) and (9, 12)? (a) 21 (b) 225 (c) 16 (d) 15
  12. 12.How far is the point (12, 16) from the origin (0, 0)? (a) 28 (b) 400 (c) 20 (d) 21
  13. 13.In which quadrant does the point (−4, −8) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  14. 14.What is the distance between the points (6, 4) and (18, 20)? (a) 400 (b) 28 (c) 20 (d) 21
  15. 15.In which quadrant does the point (7, −4) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  16. 16.In which quadrant does the point (1, −5) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  17. 17.How far is the point (6, 8) from the origin (0, 0)? (a) 10 (b) 14 (c) 100 (d) 11
  18. 18.In which quadrant does the point (2, −2) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  19. 19.What is the midpoint of the line joining (10, 8) and (16, 18)? (a) (3, 5) (b) (26, 26) (c) (13, 13) (d) (14, 13)
  20. 20.In which quadrant does the point (6, 2) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  21. 21.How far is the point (8, 15) from the origin (0, 0)? (a) 23 (b) 17 (c) 289 (d) 18
  22. 22.How far is the point (5, 12) from the origin (0, 0)? (a) 17 (b) 14 (c) 13 (d) 169
  23. 23.What is the midpoint of the line joining (5, 10) and (9, 2)? (a) (7, 6) (b) (6, 7) (c) (14, 12) (d) (2, 4)
  24. 24.What is the midpoint of the line joining (3, 11) and (5, 5)? (a) (8, 4) (b) (8, 16) (c) (4, 8) (d) (1, 3)
  25. 25.What is the distance between the points (8, 22) and (20, 6)? (a) 400 (b) 21 (c) 20 (d) 28
  26. 26.What is the distance between the points (2, 15) and (10, 9)? (a) 14 (b) 10 (c) 100 (d) 11
  27. 27.What is the distance between the points (7, 1) and (10, 5)? (a) 5 (b) 25 (c) 7 (d) 6
  28. 28.What is the distance between the points (0, 17) and (8, 2)? (a) 289 (b) 18 (c) 17 (d) 23
  29. 29.What is the midpoint of the line joining (0, 0) and (4, 12)? (a) (6, 2) (b) (3, 6) (c) (2, 6) (d) (4, 12)
  30. 30.What is the distance between the points (3, 12) and (19, 0)? (a) 20 (b) 21 (c) 400 (d) 28
  31. 31.In which quadrant does the point (−8, 2) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  32. 32.What is the distance between the points (0, 3) and (7, 27)? (a) 625 (b) 31 (c) 26 (d) 25
  33. 33.In which quadrant does the point (9, 8) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
  34. 34.How far is the point (7, 24) from the origin (0, 0)? (a) 31 (b) 625 (c) 25 (d) 26
  35. 35.What is the midpoint of the line joining (2, 15) and (4, 5)? (a) (1, 5) (b) (3, 10) (c) (10, 3) (d) (6, 20)
  36. 36.What is the midpoint of the line joining (9, 8) and (17, 4)? (a) (6, 13) (b) (13, 6) (c) (26, 12) (d) (4, 2)
  37. 37.What is the distance between the points (7, 10) and (13, 2)? (a) 10 (b) 14 (c) 11 (d) 100
  38. 38.What is the midpoint of the line joining (4, 10) and (16, 6)? (a) (8, 10) (b) (10, 8) (c) (20, 16) (d) (6, 2)
  39. 39.How far is the point (8, 6) from the origin (0, 0)? (a) 10 (b) 14 (c) 11 (d) 100
  40. 40.What is the midpoint of the line joining (6, 20) and (16, 10)? (a) (15, 11) (b) (22, 30) (c) (11, 15) (d) (5, 5)

Answer key

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

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