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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 321 · 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 midpoint of the line joining (9, 12) and (21, 0)? (a) (15, 6) (b) (6, 6) (c) (30, 12) (d) (6, 15)
  2. 2.How far is the point (5, 12) from the origin (0, 0)? (a) 13 (b) 169 (c) 17 (d) 14
  3. 3.In which quadrant does the point (1, 8) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  4. 4.What is the distance between the points (8, 12) and (17, 0)? (a) 225 (b) 21 (c) 16 (d) 15
  5. 5.What is the distance between the points (0, 2) and (16, 14)? (a) 20 (b) 400 (c) 28 (d) 21
  6. 6.What is the distance between the points (1, 2) and (7, 10)? (a) 100 (b) 14 (c) 10 (d) 11
  7. 7.What is the distance between the points (2, 5) and (10, 20)? (a) 17 (b) 18 (c) 289 (d) 23
  8. 8.What is the distance between the points (1, 0) and (25, 7)? (a) 625 (b) 26 (c) 31 (d) 25
  9. 9.In which quadrant does the point (7, 8) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  10. 10.In which quadrant does the point (4, −6) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  11. 11.How far is the point (3, 4) from the origin (0, 0)? (a) 7 (b) 25 (c) 5 (d) 6
  12. 12.What is the midpoint of the line joining (4, 2) and (10, 0)? (a) (7, 1) (b) (1, 7) (c) (14, 2) (d) (3, 1)
  13. 13.What is the midpoint of the line joining (10, 10) and (12, 4)? (a) (1, 3) (b) (11, 7) (c) (7, 11) (d) (22, 14)
  14. 14.In which quadrant does the point (5, 3) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  15. 15.In which quadrant does the point (−4, −5) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  16. 16.What is the midpoint of the line joining (0, 6) and (2, 2)? (a) (1, 2) (b) (2, 8) (c) (4, 1) (d) (1, 4)
  17. 17.What is the midpoint of the line joining (3, 2) and (7, 10)? (a) (2, 4) (b) (6, 5) (c) (10, 12) (d) (5, 6)
  18. 18.What is the midpoint of the line joining (2, 7) and (12, 13)? (a) (5, 3) (b) (7, 10) (c) (10, 7) (d) (14, 20)
  19. 19.What is the midpoint of the line joining (5, 6) and (9, 14)? (a) (10, 7) (b) (14, 20) (c) (7, 10) (d) (2, 4)
  20. 20.In which quadrant does the point (−2, 1) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  21. 21.What is the midpoint of the line joining (2, 10) and (4, 18)? (a) (1, 4) (b) (6, 28) (c) (14, 3) (d) (3, 14)
  22. 22.What is the distance between the points (7, 21) and (16, 9)? (a) 15 (b) 225 (c) 16 (d) 21
  23. 23.What is the midpoint of the line joining (1, 13) and (11, 1)? (a) (6, 7) (b) (7, 6) (c) (5, 6) (d) (12, 14)
  24. 24.What is the distance between the points (4, 10) and (28, 3)? (a) 31 (b) 625 (c) 26 (d) 25
  25. 25.How far is the point (4, 3) from the origin (0, 0)? (a) 6 (b) 5 (c) 25 (d) 7
  26. 26.In which quadrant does the point (−8, −6) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  27. 27.How far is the point (12, 9) from the origin (0, 0)? (a) 15 (b) 21 (c) 16 (d) 225
  28. 28.What is the distance between the points (7, 1) and (22, 9)? (a) 23 (b) 289 (c) 18 (d) 17
  29. 29.What is the midpoint of the line joining (10, 1) and (14, 5)? (a) (3, 12) (b) (24, 6) (c) (2, 2) (d) (12, 3)
  30. 30.What is the distance between the points (4, 25) and (16, 9)? (a) 21 (b) 28 (c) 20 (d) 400
  31. 31.What is the midpoint of the line joining (7, 18) and (11, 10)? (a) (14, 9) (b) (2, 4) (c) (18, 28) (d) (9, 14)
  32. 32.What is the distance between the points (5, 7) and (17, 16)? (a) 225 (b) 15 (c) 21 (d) 16
  33. 33.What is the midpoint of the line joining (8, 3) and (16, 15)? (a) (9, 12) (b) (4, 6) (c) (12, 9) (d) (24, 18)
  34. 34.In which quadrant does the point (3, 5) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  35. 35.How far is the point (15, 8) from the origin (0, 0)? (a) 289 (b) 17 (c) 18 (d) 23
  36. 36.In which quadrant does the point (−2, 4) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  37. 37.In which quadrant does the point (1, 5) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  38. 38.In which quadrant does the point (1, 3) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  39. 39.In which quadrant does the point (4, 7) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  40. 40.How far is the point (16, 12) from the origin (0, 0)? (a) 400 (b) 28 (c) 21 (d) 20

Answer key

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

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