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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 811 · 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.How far is the point (6, 8) from the origin (0, 0)? (a) 11 (b) 14 (c) 10 (d) 100
  2. 2.In which quadrant does the point (6, 7) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  3. 3.What is the distance between the points (7, 13) and (12, 1)? (a) 14 (b) 13 (c) 17 (d) 169
  4. 4.What is the distance between the points (7, 13) and (13, 5)? (a) 14 (b) 100 (c) 10 (d) 11
  5. 5.How far is the point (8, 6) from the origin (0, 0)? (a) 10 (b) 11 (c) 100 (d) 14
  6. 6.What is the midpoint of the line joining (8, 8) and (16, 20)? (a) (14, 12) (b) (4, 6) (c) (24, 28) (d) (12, 14)
  7. 7.What is the distance between the points (8, 25) and (15, 1)? (a) 25 (b) 26 (c) 625 (d) 31
  8. 8.What is the midpoint of the line joining (0, 15) and (8, 9)? (a) (8, 24) (b) (12, 4) (c) (4, 12) (d) (4, 3)
  9. 9.In which quadrant does the point (1, −7) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  10. 10.What is the distance between the points (5, 0) and (14, 12)? (a) 21 (b) 15 (c) 16 (d) 225
  11. 11.What is the distance between the points (3, 1) and (6, 5)? (a) 5 (b) 25 (c) 6 (d) 7
  12. 12.What is the distance between the points (7, 4) and (14, 28)? (a) 31 (b) 25 (c) 625 (d) 26
  13. 13.In which quadrant does the point (4, −9) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  14. 14.What is the distance between the points (1, 15) and (6, 3)? (a) 17 (b) 169 (c) 14 (d) 13
  15. 15.In which quadrant does the point (−5, 5) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  16. 16.What is the distance between the points (8, 15) and (17, 3)? (a) 16 (b) 21 (c) 15 (d) 225
  17. 17.What is the distance between the points (8, 0) and (16, 15)? (a) 289 (b) 23 (c) 17 (d) 18
  18. 18.What is the midpoint of the line joining (7, 0) and (19, 2)? (a) (6, 1) (b) (1, 13) (c) (13, 1) (d) (26, 2)
  19. 19.How far is the point (4, 3) from the origin (0, 0)? (a) 6 (b) 5 (c) 25 (d) 7
  20. 20.What is the distance between the points (9, 6) and (24, 14)? (a) 23 (b) 18 (c) 17 (d) 289
  21. 21.What is the midpoint of the line joining (1, 13) and (7, 9)? (a) (4, 11) (b) (8, 22) (c) (3, 2) (d) (11, 4)
  22. 22.What is the distance between the points (7, 19) and (16, 7)? (a) 16 (b) 15 (c) 225 (d) 21
  23. 23.In which quadrant does the point (−7, 1) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  24. 24.What is the distance between the points (7, 17) and (16, 5)? (a) 21 (b) 225 (c) 15 (d) 16
  25. 25.In which quadrant does the point (1, −9) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  26. 26.What is the distance between the points (6, 7) and (14, 22)? (a) 23 (b) 289 (c) 18 (d) 17
  27. 27.What is the midpoint of the line joining (10, 1) and (22, 7)? (a) (4, 16) (b) (6, 3) (c) (32, 8) (d) (16, 4)
  28. 28.What is the midpoint of the line joining (9, 2) and (15, 12)? (a) (7, 12) (b) (12, 7) (c) (3, 5) (d) (24, 14)
  29. 29.In which quadrant does the point (−2, −3) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  30. 30.What is the midpoint of the line joining (3, 13) and (9, 1)? (a) (12, 14) (b) (3, 6) (c) (7, 6) (d) (6, 7)
  31. 31.What is the distance between the points (2, 5) and (18, 17)? (a) 400 (b) 20 (c) 28 (d) 21
  32. 32.In which quadrant does the point (9, 4) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  33. 33.What is the midpoint of the line joining (8, 0) and (20, 12)? (a) (6, 6) (b) (6, 14) (c) (28, 12) (d) (14, 6)
  34. 34.What is the distance between the points (2, 9) and (14, 25)? (a) 28 (b) 20 (c) 21 (d) 400
  35. 35.What is the distance between the points (0, 18) and (16, 6)? (a) 400 (b) 28 (c) 20 (d) 21
  36. 36.How far is the point (8, 15) from the origin (0, 0)? (a) 17 (b) 18 (c) 23 (d) 289
  37. 37.What is the distance between the points (3, 12) and (27, 5)? (a) 31 (b) 625 (c) 25 (d) 26
  38. 38.What is the distance between the points (7, 5) and (11, 2)? (a) 7 (b) 25 (c) 5 (d) 6
  39. 39.In which quadrant does the point (−4, −5) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  40. 40.What is the distance between the points (0, 28) and (7, 4)? (a) 625 (b) 26 (c) 31 (d) 25

Answer key

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

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