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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 689 · 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 (5, 12) from the origin (0, 0)? (a) 169 (b) 14 (c) 13 (d) 17
  2. 2.In which quadrant does the point (−3, −2) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  3. 3.How far is the point (8, 15) from the origin (0, 0)? (a) 289 (b) 23 (c) 18 (d) 17
  4. 4.What is the distance between the points (6, 8) and (14, 2)? (a) 14 (b) 11 (c) 100 (d) 10
  5. 5.How far is the point (8, 6) from the origin (0, 0)? (a) 100 (b) 14 (c) 11 (d) 10
  6. 6.What is the distance between the points (1, 17) and (6, 5)? (a) 169 (b) 17 (c) 14 (d) 13
  7. 7.What is the distance between the points (6, 9) and (10, 6)? (a) 5 (b) 25 (c) 6 (d) 7
  8. 8.In which quadrant does the point (−2, 9) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  9. 9.What is the distance between the points (1, 3) and (9, 9)? (a) 10 (b) 100 (c) 14 (d) 11
  10. 10.What is the distance between the points (8, 1) and (11, 5)? (a) 25 (b) 6 (c) 5 (d) 7
  11. 11.What is the distance between the points (7, 3) and (15, 18)? (a) 23 (b) 289 (c) 18 (d) 17
  12. 12.How far is the point (7, 24) from the origin (0, 0)? (a) 31 (b) 625 (c) 26 (d) 25
  13. 13.What is the midpoint of the line joining (5, 0) and (9, 4)? (a) (7, 2) (b) (14, 4) (c) (2, 7) (d) (2, 2)
  14. 14.What is the midpoint of the line joining (7, 10) and (19, 20)? (a) (13, 15) (b) (15, 13) (c) (6, 5) (d) (26, 30)
  15. 15.What is the midpoint of the line joining (10, 2) and (14, 0)? (a) (1, 12) (b) (12, 1) (c) (2, 1) (d) (24, 2)
  16. 16.What is the midpoint of the line joining (10, 1) and (12, 7)? (a) (4, 11) (b) (1, 3) (c) (11, 4) (d) (22, 8)
  17. 17.What is the distance between the points (6, 17) and (14, 2)? (a) 18 (b) 23 (c) 289 (d) 17
  18. 18.What is the distance between the points (2, 7) and (14, 23)? (a) 20 (b) 28 (c) 21 (d) 400
  19. 19.In which quadrant does the point (−7, −4) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  20. 20.What is the midpoint of the line joining (9, 1) and (17, 11)? (a) (26, 12) (b) (6, 13) (c) (13, 6) (d) (4, 5)
  21. 21.What is the midpoint of the line joining (8, 9) and (12, 1)? (a) (5, 10) (b) (20, 10) (c) (2, 4) (d) (10, 5)
  22. 22.What is the distance between the points (5, 17) and (21, 5)? (a) 21 (b) 400 (c) 20 (d) 28
  23. 23.What is the distance between the points (2, 30) and (9, 6)? (a) 31 (b) 625 (c) 26 (d) 25
  24. 24.In which quadrant does the point (−8, −6) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  25. 25.What is the distance between the points (9, 4) and (17, 10)? (a) 11 (b) 100 (c) 14 (d) 10
  26. 26.In which quadrant does the point (6, −4) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  27. 27.What is the distance between the points (2, 13) and (26, 6)? (a) 26 (b) 31 (c) 25 (d) 625
  28. 28.How far is the point (3, 4) from the origin (0, 0)? (a) 25 (b) 5 (c) 6 (d) 7
  29. 29.In which quadrant does the point (−6, −7) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  30. 30.What is the distance between the points (3, 0) and (27, 7)? (a) 26 (b) 25 (c) 31 (d) 625
  31. 31.What is the midpoint of the line joining (10, 13) and (14, 1)? (a) (2, 6) (b) (24, 14) (c) (7, 12) (d) (12, 7)
  32. 32.In which quadrant does the point (−5, −9) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  33. 33.What is the midpoint of the line joining (1, 0) and (5, 6)? (a) (2, 3) (b) (6, 6) (c) (4, 3) (d) (3, 3)
  34. 34.What is the distance between the points (9, 8) and (17, 23)? (a) 17 (b) 289 (c) 18 (d) 23
  35. 35.How far is the point (15, 8) from the origin (0, 0)? (a) 289 (b) 18 (c) 23 (d) 17
  36. 36.In which quadrant does the point (−6, −9) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
  37. 37.What is the distance between the points (3, 9) and (9, 1)? (a) 14 (b) 11 (c) 100 (d) 10
  38. 38.What is the distance between the points (6, 17) and (18, 8)? (a) 15 (b) 21 (c) 225 (d) 16
  39. 39.What is the midpoint of the line joining (9, 10) and (21, 8)? (a) (6, 1) (b) (30, 18) (c) (15, 9) (d) (9, 15)
  40. 40.What is the distance between the points (1, 4) and (13, 9)? (a) 14 (b) 13 (c) 169 (d) 17

Answer key

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

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