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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 251 · 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) 100 (b) 14 (c) 11 (d) 10
  2. 2.What is the midpoint of the line joining (10, 3) and (20, 11)? (a) (5, 4) (b) (7, 15) (c) (15, 7) (d) (30, 14)
  3. 3.What is the midpoint of the line joining (8, 9) and (10, 17)? (a) (13, 9) (b) (18, 26) (c) (1, 4) (d) (9, 13)
  4. 4.What is the distance between the points (7, 12) and (13, 4)? (a) 14 (b) 11 (c) 10 (d) 100
  5. 5.In which quadrant does the point (−9, 1) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  6. 6.In which quadrant does the point (8, 3) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  7. 7.What is the midpoint of the line joining (10, 2) and (12, 10)? (a) (22, 12) (b) (1, 4) (c) (6, 11) (d) (11, 6)
  8. 8.How far is the point (3, 4) from the origin (0, 0)? (a) 5 (b) 25 (c) 6 (d) 7
  9. 9.What is the midpoint of the line joining (2, 6) and (4, 16)? (a) (3, 11) (b) (1, 5) (c) (11, 3) (d) (6, 22)
  10. 10.In which quadrant does the point (2, 5) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  11. 11.What is the midpoint of the line joining (9, 10) and (13, 16)? (a) (11, 13) (b) (2, 3) (c) (13, 11) (d) (22, 26)
  12. 12.What is the distance between the points (1, 1) and (8, 25)? (a) 26 (b) 625 (c) 25 (d) 31
  13. 13.What is the midpoint of the line joining (7, 6) and (19, 8)? (a) (6, 1) (b) (7, 13) (c) (13, 7) (d) (26, 14)
  14. 14.What is the distance between the points (9, 11) and (17, 5)? (a) 11 (b) 100 (c) 10 (d) 14
  15. 15.What is the midpoint of the line joining (1, 21) and (7, 9)? (a) (4, 15) (b) (15, 4) (c) (3, 6) (d) (8, 30)
  16. 16.How far is the point (12, 16) from the origin (0, 0)? (a) 20 (b) 28 (c) 21 (d) 400
  17. 17.In which quadrant does the point (−8, −5) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  18. 18.What is the distance between the points (4, 8) and (12, 23)? (a) 17 (b) 18 (c) 23 (d) 289
  19. 19.In which quadrant does the point (3, 1) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  20. 20.What is the distance between the points (9, 13) and (12, 9)? (a) 6 (b) 7 (c) 5 (d) 25
  21. 21.What is the midpoint of the line joining (5, 6) and (17, 0)? (a) (3, 11) (b) (6, 3) (c) (11, 3) (d) (22, 6)
  22. 22.What is the distance between the points (0, 4) and (8, 19)? (a) 18 (b) 23 (c) 17 (d) 289
  23. 23.What is the distance between the points (1, 0) and (7, 8)? (a) 100 (b) 14 (c) 11 (d) 10
  24. 24.What is the midpoint of the line joining (2, 5) and (6, 9)? (a) (4, 7) (b) (7, 4) (c) (8, 14) (d) (2, 2)
  25. 25.What is the distance between the points (9, 4) and (25, 16)? (a) 28 (b) 21 (c) 20 (d) 400
  26. 26.What is the distance between the points (7, 0) and (19, 9)? (a) 16 (b) 15 (c) 21 (d) 225
  27. 27.How far is the point (24, 7) from the origin (0, 0)? (a) 625 (b) 26 (c) 31 (d) 25
  28. 28.What is the distance between the points (9, 7) and (21, 2)? (a) 169 (b) 13 (c) 17 (d) 14
  29. 29.How far is the point (4, 3) from the origin (0, 0)? (a) 5 (b) 6 (c) 7 (d) 25
  30. 30.What is the distance between the points (1, 2) and (4, 6)? (a) 5 (b) 25 (c) 7 (d) 6
  31. 31.What is the midpoint of the line joining (2, 4) and (14, 12)? (a) (6, 4) (b) (16, 16) (c) (9, 8) (d) (8, 8)
  32. 32.What is the midpoint of the line joining (2, 7) and (14, 1)? (a) (16, 8) (b) (8, 4) (c) (4, 8) (d) (6, 3)
  33. 33.How far is the point (16, 12) from the origin (0, 0)? (a) 20 (b) 21 (c) 400 (d) 28
  34. 34.In which quadrant does the point (5, 1) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  35. 35.What is the midpoint of the line joining (4, 2) and (10, 6)? (a) (7, 4) (b) (3, 2) (c) (14, 8) (d) (4, 7)
  36. 36.In which quadrant does the point (3, −9) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
  37. 37.In which quadrant does the point (5, −2) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  38. 38.What is the distance between the points (5, 8) and (17, 13)? (a) 14 (b) 17 (c) 13 (d) 169
  39. 39.How far is the point (12, 5) from the origin (0, 0)? (a) 17 (b) 169 (c) 13 (d) 14
  40. 40.What is the distance between the points (8, 12) and (20, 7)? (a) 17 (b) 13 (c) 169 (d) 14

Answer key

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

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