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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 95 · 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 (7, 24) from the origin (0, 0)? (a) 31 (b) 25 (c) 625 (d) 26
  2. 2.How far is the point (8, 6) from the origin (0, 0)? (a) 10 (b) 14 (c) 11 (d) 100
  3. 3.In which quadrant does the point (5, 9) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  4. 4.In which quadrant does the point (−6, 2) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  5. 5.How far is the point (8, 15) from the origin (0, 0)? (a) 23 (b) 18 (c) 289 (d) 17
  6. 6.How far is the point (3, 4) from the origin (0, 0)? (a) 7 (b) 5 (c) 6 (d) 25
  7. 7.What is the midpoint of the line joining (7, 2) and (19, 0)? (a) (13, 1) (b) (6, 1) (c) (26, 2) (d) (1, 13)
  8. 8.What is the midpoint of the line joining (8, 3) and (12, 11)? (a) (20, 14) (b) (2, 4) (c) (10, 7) (d) (7, 10)
  9. 9.In which quadrant does the point (−5, −2) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  10. 10.How far is the point (9, 12) from the origin (0, 0)? (a) 15 (b) 16 (c) 225 (d) 21
  11. 11.What is the distance between the points (9, 5) and (12, 1)? (a) 25 (b) 5 (c) 6 (d) 7
  12. 12.What is the midpoint of the line joining (7, 6) and (19, 16)? (a) (11, 13) (b) (26, 22) (c) (13, 11) (d) (6, 5)
  13. 13.In which quadrant does the point (−4, 4) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  14. 14.What is the midpoint of the line joining (1, 1) and (7, 7)? (a) (3, 3) (b) (8, 8) (c) (5, 4) (d) (4, 4)
  15. 15.In which quadrant does the point (−3, −2) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  16. 16.What is the distance between the points (5, 12) and (14, 0)? (a) 15 (b) 21 (c) 16 (d) 225
  17. 17.How far is the point (12, 9) from the origin (0, 0)? (a) 16 (b) 15 (c) 21 (d) 225
  18. 18.What is the distance between the points (4, 0) and (13, 12)? (a) 15 (b) 16 (c) 225 (d) 21
  19. 19.What is the midpoint of the line joining (0, 9) and (6, 21)? (a) (3, 6) (b) (6, 30) (c) (15, 3) (d) (3, 15)
  20. 20.What is the midpoint of the line joining (3, 8) and (7, 2)? (a) (2, 3) (b) (10, 10) (c) (6, 5) (d) (5, 5)
  21. 21.How far is the point (12, 5) from the origin (0, 0)? (a) 17 (b) 13 (c) 169 (d) 14
  22. 22.In which quadrant does the point (−2, 4) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  23. 23.What is the midpoint of the line joining (2, 8) and (14, 18)? (a) (16, 26) (b) (13, 8) (c) (8, 13) (d) (6, 5)
  24. 24.What is the midpoint of the line joining (2, 11) and (12, 5)? (a) (8, 7) (b) (5, 3) (c) (7, 8) (d) (14, 16)
  25. 25.What is the distance between the points (8, 0) and (24, 12)? (a) 28 (b) 21 (c) 400 (d) 20
  26. 26.What is the midpoint of the line joining (10, 12) and (18, 4)? (a) (8, 14) (b) (4, 4) (c) (28, 16) (d) (14, 8)
  27. 27.What is the midpoint of the line joining (2, 5) and (14, 13)? (a) (8, 9) (b) (16, 18) (c) (9, 8) (d) (6, 4)
  28. 28.What is the distance between the points (9, 0) and (21, 16)? (a) 20 (b) 400 (c) 21 (d) 28
  29. 29.In which quadrant does the point (2, 9) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  30. 30.In which quadrant does the point (−9, −2) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  31. 31.In which quadrant does the point (−3, 9) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  32. 32.What is the distance between the points (4, 19) and (16, 3)? (a) 21 (b) 20 (c) 28 (d) 400
  33. 33.How far is the point (6, 8) from the origin (0, 0)? (a) 11 (b) 14 (c) 10 (d) 100
  34. 34.What is the distance between the points (5, 13) and (13, 7)? (a) 100 (b) 11 (c) 14 (d) 10
  35. 35.What is the distance between the points (2, 7) and (9, 31)? (a) 625 (b) 26 (c) 31 (d) 25
  36. 36.What is the midpoint of the line joining (5, 9) and (9, 17)? (a) (13, 7) (b) (2, 4) (c) (14, 26) (d) (7, 13)
  37. 37.What is the distance between the points (2, 8) and (8, 16)? (a) 11 (b) 100 (c) 10 (d) 14
  38. 38.How far is the point (4, 3) from the origin (0, 0)? (a) 25 (b) 7 (c) 5 (d) 6
  39. 39.In which quadrant does the point (−3, 6) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  40. 40.What is the distance between the points (1, 4) and (13, 13)? (a) 15 (b) 225 (c) 16 (d) 21

Answer key

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

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