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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 302 · 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 (4, 9) and (8, 1)? (a) (6, 5) (b) (12, 10) (c) (2, 4) (d) (5, 6)
  2. 2.What is the midpoint of the line joining (9, 14) and (11, 6)? (a) (10, 10) (b) (1, 4) (c) (11, 10) (d) (20, 20)
  3. 3.In which quadrant does the point (−1, 2) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  4. 4.How far is the point (24, 7) from the origin (0, 0)? (a) 31 (b) 625 (c) 26 (d) 25
  5. 5.What is the distance between the points (4, 21) and (13, 9)? (a) 16 (b) 21 (c) 15 (d) 225
  6. 6.How far is the point (12, 9) from the origin (0, 0)? (a) 16 (b) 225 (c) 15 (d) 21
  7. 7.What is the distance between the points (6, 14) and (22, 2)? (a) 20 (b) 28 (c) 400 (d) 21
  8. 8.What is the midpoint of the line joining (2, 5) and (8, 1)? (a) (5, 3) (b) (3, 2) (c) (10, 6) (d) (3, 5)
  9. 9.What is the midpoint of the line joining (4, 14) and (16, 4)? (a) (10, 9) (b) (20, 18) (c) (6, 5) (d) (9, 10)
  10. 10.What is the midpoint of the line joining (10, 0) and (20, 12)? (a) (15, 6) (b) (5, 6) (c) (30, 12) (d) (6, 15)
  11. 11.How far is the point (15, 8) from the origin (0, 0)? (a) 18 (b) 17 (c) 289 (d) 23
  12. 12.How far is the point (12, 5) from the origin (0, 0)? (a) 17 (b) 14 (c) 169 (d) 13
  13. 13.What is the midpoint of the line joining (10, 14) and (16, 2)? (a) (13, 8) (b) (8, 13) (c) (26, 16) (d) (3, 6)
  14. 14.How far is the point (16, 12) from the origin (0, 0)? (a) 20 (b) 400 (c) 28 (d) 21
  15. 15.What is the midpoint of the line joining (6, 10) and (10, 4)? (a) (2, 3) (b) (8, 7) (c) (16, 14) (d) (7, 8)
  16. 16.How far is the point (4, 3) from the origin (0, 0)? (a) 25 (b) 6 (c) 5 (d) 7
  17. 17.What is the distance between the points (8, 13) and (13, 1)? (a) 169 (b) 17 (c) 14 (d) 13
  18. 18.What is the midpoint of the line joining (6, 9) and (12, 5)? (a) (3, 2) (b) (7, 9) (c) (18, 14) (d) (9, 7)
  19. 19.In which quadrant does the point (6, −1) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  20. 20.What is the distance between the points (0, 5) and (15, 13)? (a) 23 (b) 289 (c) 18 (d) 17
  21. 21.In which quadrant does the point (1, −2) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  22. 22.How far is the point (12, 16) from the origin (0, 0)? (a) 21 (b) 20 (c) 28 (d) 400
  23. 23.What is the midpoint of the line joining (8, 6) and (10, 14)? (a) (18, 20) (b) (1, 4) (c) (10, 9) (d) (9, 10)
  24. 24.What is the midpoint of the line joining (9, 9) and (19, 5)? (a) (5, 2) (b) (14, 7) (c) (7, 14) (d) (28, 14)
  25. 25.What is the distance between the points (5, 6) and (8, 10)? (a) 6 (b) 25 (c) 5 (d) 7
  26. 26.In which quadrant does the point (−3, 1) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  27. 27.What is the distance between the points (3, 3) and (12, 15)? (a) 16 (b) 225 (c) 15 (d) 21
  28. 28.What is the midpoint of the line joining (7, 6) and (19, 14)? (a) (6, 4) (b) (26, 20) (c) (10, 13) (d) (13, 10)
  29. 29.What is the midpoint of the line joining (6, 8) and (16, 0)? (a) (11, 4) (b) (22, 8) (c) (4, 11) (d) (5, 4)
  30. 30.What is the distance between the points (3, 6) and (19, 18)? (a) 20 (b) 400 (c) 28 (d) 21
  31. 31.What is the midpoint of the line joining (3, 16) and (11, 4)? (a) (10, 7) (b) (4, 6) (c) (7, 10) (d) (14, 20)
  32. 32.What is the midpoint of the line joining (3, 15) and (5, 3)? (a) (4, 9) (b) (9, 4) (c) (1, 6) (d) (8, 18)
  33. 33.In which quadrant does the point (−5, −9) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  34. 34.In which quadrant does the point (−2, 2) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  35. 35.In which quadrant does the point (−5, 9) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  36. 36.What is the distance between the points (0, 13) and (8, 7)? (a) 100 (b) 14 (c) 11 (d) 10
  37. 37.In which quadrant does the point (−6, −6) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  38. 38.What is the midpoint of the line joining (8, 9) and (10, 13)? (a) (1, 2) (b) (11, 9) (c) (18, 22) (d) (9, 11)
  39. 39.What is the midpoint of the line joining (1, 5) and (7, 1)? (a) (3, 2) (b) (8, 6) (c) (4, 3) (d) (3, 4)
  40. 40.In which quadrant does the point (−2, −9) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant

Answer key

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

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