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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 235 · 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.What is the distance between the points (5, 4) and (8, 0)? (a) 5 (b) 25 (c) 7 (d) 6
  2. 2.In which quadrant does the point (5, 7) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  3. 3.What is the distance between the points (7, 18) and (19, 9)? (a) 16 (b) 21 (c) 225 (d) 15
  4. 4.In which quadrant does the point (5, −6) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  5. 5.In which quadrant does the point (1, −2) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  6. 6.In which quadrant does the point (3, 7) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  7. 7.How far is the point (6, 8) from the origin (0, 0)? (a) 14 (b) 11 (c) 100 (d) 10
  8. 8.What is the midpoint of the line joining (6, 14) and (8, 8)? (a) (7, 11) (b) (14, 22) (c) (11, 7) (d) (1, 3)
  9. 9.In which quadrant does the point (8, 9) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  10. 10.What is the midpoint of the line joining (3, 1) and (15, 3)? (a) (9, 2) (b) (2, 9) (c) (18, 4) (d) (6, 1)
  11. 11.How far is the point (24, 7) from the origin (0, 0)? (a) 31 (b) 625 (c) 25 (d) 26
  12. 12.What is the distance between the points (4, 3) and (8, 0)? (a) 6 (b) 5 (c) 25 (d) 7
  13. 13.In which quadrant does the point (−9, −7) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  14. 14.What is the distance between the points (9, 0) and (24, 8)? (a) 289 (b) 18 (c) 23 (d) 17
  15. 15.What is the distance between the points (2, 8) and (14, 24)? (a) 400 (b) 21 (c) 20 (d) 28
  16. 16.In which quadrant does the point (3, 5) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  17. 17.In which quadrant does the point (−7, 6) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  18. 18.In which quadrant does the point (−1, 4) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  19. 19.What is the distance between the points (5, 6) and (20, 14)? (a) 289 (b) 23 (c) 17 (d) 18
  20. 20.What is the distance between the points (2, 18) and (11, 6)? (a) 15 (b) 21 (c) 225 (d) 16
  21. 21.In which quadrant does the point (1, 1) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  22. 22.What is the distance between the points (1, 17) and (17, 5)? (a) 400 (b) 28 (c) 21 (d) 20
  23. 23.What is the midpoint of the line joining (9, 17) and (19, 5)? (a) (11, 14) (b) (5, 6) (c) (14, 11) (d) (28, 22)
  24. 24.What is the distance between the points (9, 6) and (17, 0)? (a) 10 (b) 11 (c) 14 (d) 100
  25. 25.How far is the point (5, 12) from the origin (0, 0)? (a) 13 (b) 17 (c) 14 (d) 169
  26. 26.In which quadrant does the point (−8, −6) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  27. 27.In which quadrant does the point (6, 4) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  28. 28.What is the distance between the points (5, 4) and (17, 9)? (a) 17 (b) 14 (c) 13 (d) 169
  29. 29.In which quadrant does the point (9, 4) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  30. 30.How far is the point (8, 15) from the origin (0, 0)? (a) 18 (b) 289 (c) 17 (d) 23
  31. 31.In which quadrant does the point (6, 2) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  32. 32.What is the distance between the points (9, 1) and (17, 16)? (a) 289 (b) 17 (c) 23 (d) 18
  33. 33.What is the distance between the points (9, 7) and (33, 0)? (a) 25 (b) 26 (c) 625 (d) 31
  34. 34.What is the distance between the points (0, 0) and (7, 24)? (a) 625 (b) 31 (c) 25 (d) 26
  35. 35.In which quadrant does the point (−5, 2) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  36. 36.In which quadrant does the point (−3, 3) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  37. 37.What is the distance between the points (7, 15) and (16, 3)? (a) 225 (b) 15 (c) 16 (d) 21
  38. 38.How far is the point (12, 16) from the origin (0, 0)? (a) 28 (b) 20 (c) 21 (d) 400
  39. 39.What is the midpoint of the line joining (1, 0) and (5, 2)? (a) (2, 1) (b) (6, 2) (c) (3, 1) (d) (1, 3)
  40. 40.What is the distance between the points (2, 5) and (5, 9)? (a) 5 (b) 25 (c) 7 (d) 6

Answer key

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

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