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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 197 · 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.In which quadrant does the point (−6, −6) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  2. 2.How far is the point (8, 15) from the origin (0, 0)? (a) 289 (b) 18 (c) 23 (d) 17
  3. 3.What is the distance between the points (5, 10) and (9, 7)? (a) 6 (b) 7 (c) 25 (d) 5
  4. 4.How far is the point (6, 8) from the origin (0, 0)? (a) 10 (b) 100 (c) 14 (d) 11
  5. 5.How far is the point (3, 4) from the origin (0, 0)? (a) 25 (b) 5 (c) 6 (d) 7
  6. 6.What is the distance between the points (5, 8) and (17, 3)? (a) 17 (b) 169 (c) 14 (d) 13
  7. 7.What is the distance between the points (0, 0) and (9, 12)? (a) 16 (b) 225 (c) 21 (d) 15
  8. 8.What is the midpoint of the line joining (10, 4) and (14, 6)? (a) (12, 5) (b) (24, 10) (c) (2, 1) (d) (5, 12)
  9. 9.What is the midpoint of the line joining (4, 2) and (8, 0)? (a) (2, 1) (b) (6, 1) (c) (1, 6) (d) (12, 2)
  10. 10.What is the distance between the points (4, 18) and (16, 2)? (a) 28 (b) 20 (c) 21 (d) 400
  11. 11.How far is the point (15, 8) from the origin (0, 0)? (a) 18 (b) 23 (c) 17 (d) 289
  12. 12.How far is the point (24, 7) from the origin (0, 0)? (a) 31 (b) 625 (c) 26 (d) 25
  13. 13.What is the distance between the points (4, 4) and (28, 11)? (a) 25 (b) 31 (c) 625 (d) 26
  14. 14.In which quadrant does the point (9, −7) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  15. 15.In which quadrant does the point (−4, −1) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
  16. 16.How far is the point (8, 6) from the origin (0, 0)? (a) 14 (b) 10 (c) 11 (d) 100
  17. 17.What is the midpoint of the line joining (1, 9) and (3, 19)? (a) (2, 14) (b) (1, 5) (c) (14, 2) (d) (4, 28)
  18. 18.How far is the point (9, 12) from the origin (0, 0)? (a) 15 (b) 16 (c) 225 (d) 21
  19. 19.What is the midpoint of the line joining (2, 2) and (8, 0)? (a) (10, 2) (b) (3, 1) (c) (1, 5) (d) (5, 1)
  20. 20.In which quadrant does the point (−2, −4) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  21. 21.In which quadrant does the point (4, 5) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  22. 22.How far is the point (7, 24) from the origin (0, 0)? (a) 31 (b) 625 (c) 26 (d) 25
  23. 23.In which quadrant does the point (6, −4) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  24. 24.What is the distance between the points (1, 32) and (8, 8)? (a) 26 (b) 625 (c) 31 (d) 25
  25. 25.In which quadrant does the point (−5, 6) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  26. 26.In which quadrant does the point (6, −9) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  27. 27.What is the midpoint of the line joining (4, 9) and (12, 17)? (a) (8, 13) (b) (13, 8) (c) (4, 4) (d) (16, 26)
  28. 28.What is the distance between the points (0, 14) and (6, 6)? (a) 11 (b) 14 (c) 100 (d) 10
  29. 29.What is the distance between the points (9, 14) and (18, 2)? (a) 21 (b) 16 (c) 15 (d) 225
  30. 30.What is the distance between the points (8, 1) and (24, 13)? (a) 21 (b) 400 (c) 28 (d) 20
  31. 31.What is the distance between the points (0, 10) and (3, 6)? (a) 5 (b) 6 (c) 7 (d) 25
  32. 32.What is the distance between the points (9, 9) and (25, 21)? (a) 28 (b) 20 (c) 21 (d) 400
  33. 33.What is the distance between the points (1, 26) and (8, 2)? (a) 26 (b) 31 (c) 625 (d) 25
  34. 34.What is the distance between the points (3, 5) and (15, 21)? (a) 21 (b) 20 (c) 400 (d) 28
  35. 35.What is the distance between the points (1, 9) and (25, 16)? (a) 26 (b) 625 (c) 31 (d) 25
  36. 36.In which quadrant does the point (−1, −8) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  37. 37.What is the midpoint of the line joining (0, 3) and (4, 15)? (a) (9, 2) (b) (4, 18) (c) (2, 6) (d) (2, 9)
  38. 38.What is the distance between the points (9, 11) and (15, 3)? (a) 100 (b) 14 (c) 10 (d) 11
  39. 39.What is the distance between the points (5, 7) and (12, 31)? (a) 625 (b) 31 (c) 26 (d) 25
  40. 40.What is the midpoint of the line joining (10, 18) and (12, 6)? (a) (22, 24) (b) (12, 11) (c) (11, 12) (d) (1, 6)

Answer key

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

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