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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 959 · 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 (3, −6) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  2. 2.How far is the point (12, 9) from the origin (0, 0)? (a) 15 (b) 21 (c) 225 (d) 16
  3. 3.What is the distance between the points (7, 2) and (22, 10)? (a) 23 (b) 18 (c) 289 (d) 17
  4. 4.What is the distance between the points (9, 24) and (21, 8)? (a) 28 (b) 400 (c) 21 (d) 20
  5. 5.What is the distance between the points (3, 10) and (15, 5)? (a) 14 (b) 17 (c) 13 (d) 169
  6. 6.What is the distance between the points (6, 12) and (10, 9)? (a) 7 (b) 6 (c) 5 (d) 25
  7. 7.What is the distance between the points (1, 7) and (16, 15)? (a) 289 (b) 23 (c) 18 (d) 17
  8. 8.In which quadrant does the point (−6, −8) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  9. 9.In which quadrant does the point (−6, −3) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  10. 10.What is the distance between the points (1, 14) and (6, 2)? (a) 14 (b) 13 (c) 17 (d) 169
  11. 11.In which quadrant does the point (3, −9) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  12. 12.How far is the point (8, 6) from the origin (0, 0)? (a) 100 (b) 10 (c) 14 (d) 11
  13. 13.In which quadrant does the point (−4, −2) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  14. 14.What is the midpoint of the line joining (10, 22) and (22, 10)? (a) (17, 16) (b) (32, 32) (c) (16, 16) (d) (6, 6)
  15. 15.What is the distance between the points (2, 0) and (14, 16)? (a) 21 (b) 20 (c) 28 (d) 400
  16. 16.What is the midpoint of the line joining (1, 4) and (11, 2)? (a) (3, 6) (b) (12, 6) (c) (5, 1) (d) (6, 3)
  17. 17.What is the distance between the points (9, 1) and (17, 16)? (a) 18 (b) 17 (c) 23 (d) 289
  18. 18.How far is the point (3, 4) from the origin (0, 0)? (a) 7 (b) 5 (c) 25 (d) 6
  19. 19.What is the midpoint of the line joining (8, 1) and (16, 9)? (a) (5, 12) (b) (24, 10) (c) (12, 5) (d) (4, 4)
  20. 20.What is the distance between the points (0, 7) and (15, 15)? (a) 17 (b) 289 (c) 18 (d) 23
  21. 21.What is the midpoint of the line joining (4, 3) and (6, 11)? (a) (1, 4) (b) (5, 7) (c) (7, 5) (d) (10, 14)
  22. 22.What is the midpoint of the line joining (2, 7) and (6, 11)? (a) (2, 2) (b) (9, 4) (c) (8, 18) (d) (4, 9)
  23. 23.What is the midpoint of the line joining (7, 11) and (9, 7)? (a) (8, 9) (b) (1, 2) (c) (16, 18) (d) (9, 8)
  24. 24.What is the distance between the points (2, 7) and (6, 4)? (a) 25 (b) 6 (c) 7 (d) 5
  25. 25.In which quadrant does the point (−9, −2) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  26. 26.What is the distance between the points (7, 1) and (19, 10)? (a) 21 (b) 225 (c) 16 (d) 15
  27. 27.How far is the point (5, 12) from the origin (0, 0)? (a) 17 (b) 14 (c) 169 (d) 13
  28. 28.What is the distance between the points (5, 20) and (21, 8)? (a) 20 (b) 28 (c) 21 (d) 400
  29. 29.What is the midpoint of the line joining (8, 9) and (20, 7)? (a) (6, 1) (b) (8, 14) (c) (28, 16) (d) (14, 8)
  30. 30.What is the midpoint of the line joining (3, 21) and (7, 9)? (a) (5, 15) (b) (2, 6) (c) (10, 30) (d) (15, 5)
  31. 31.What is the midpoint of the line joining (2, 2) and (14, 10)? (a) (8, 6) (b) (16, 12) (c) (6, 4) (d) (6, 8)
  32. 32.What is the midpoint of the line joining (7, 0) and (15, 8)? (a) (4, 11) (b) (22, 8) (c) (4, 4) (d) (11, 4)
  33. 33.What is the distance between the points (1, 16) and (13, 0)? (a) 400 (b) 21 (c) 28 (d) 20
  34. 34.How far is the point (15, 8) from the origin (0, 0)? (a) 23 (b) 18 (c) 289 (d) 17
  35. 35.In which quadrant does the point (2, −5) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  36. 36.What is the midpoint of the line joining (5, 11) and (13, 5)? (a) (18, 16) (b) (4, 3) (c) (9, 8) (d) (8, 9)
  37. 37.What is the midpoint of the line joining (7, 0) and (11, 4)? (a) (2, 2) (b) (9, 2) (c) (18, 4) (d) (2, 9)
  38. 38.In which quadrant does the point (−7, 5) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  39. 39.How far is the point (6, 8) from the origin (0, 0)? (a) 100 (b) 14 (c) 11 (d) 10
  40. 40.How far is the point (12, 5) from the origin (0, 0)? (a) 17 (b) 14 (c) 13 (d) 169

Answer key

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

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