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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 612 · 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 (−8, −9) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  2. 2.What is the midpoint of the line joining (10, 9) and (14, 7)? (a) (2, 1) (b) (24, 16) (c) (12, 8) (d) (8, 12)
  3. 3.What is the midpoint of the line joining (2, 8) and (8, 0)? (a) (4, 5) (b) (10, 8) (c) (5, 4) (d) (3, 4)
  4. 4.How far is the point (16, 12) from the origin (0, 0)? (a) 28 (b) 21 (c) 400 (d) 20
  5. 5.How far is the point (9, 12) from the origin (0, 0)? (a) 225 (b) 21 (c) 15 (d) 16
  6. 6.What is the distance between the points (9, 3) and (25, 15)? (a) 400 (b) 28 (c) 21 (d) 20
  7. 7.In which quadrant does the point (4, −5) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  8. 8.In which quadrant does the point (−1, −2) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  9. 9.How far is the point (15, 8) from the origin (0, 0)? (a) 23 (b) 289 (c) 17 (d) 18
  10. 10.What is the distance between the points (1, 18) and (9, 3)? (a) 18 (b) 289 (c) 17 (d) 23
  11. 11.What is the midpoint of the line joining (0, 10) and (8, 2)? (a) (4, 6) (b) (8, 12) (c) (4, 4) (d) (6, 4)
  12. 12.How far is the point (5, 12) from the origin (0, 0)? (a) 169 (b) 13 (c) 17 (d) 14
  13. 13.What is the distance between the points (2, 6) and (10, 0)? (a) 10 (b) 14 (c) 11 (d) 100
  14. 14.What is the midpoint of the line joining (3, 5) and (7, 3)? (a) (4, 5) (b) (10, 8) (c) (2, 1) (d) (5, 4)
  15. 15.How far is the point (12, 16) from the origin (0, 0)? (a) 28 (b) 20 (c) 400 (d) 21
  16. 16.What is the distance between the points (2, 10) and (14, 1)? (a) 15 (b) 21 (c) 16 (d) 225
  17. 17.What is the distance between the points (5, 9) and (17, 25)? (a) 400 (b) 20 (c) 28 (d) 21
  18. 18.What is the midpoint of the line joining (10, 12) and (14, 10)? (a) (2, 1) (b) (24, 22) (c) (11, 12) (d) (12, 11)
  19. 19.How far is the point (7, 24) from the origin (0, 0)? (a) 26 (b) 31 (c) 25 (d) 625
  20. 20.What is the midpoint of the line joining (8, 3) and (12, 5)? (a) (20, 8) (b) (2, 1) (c) (4, 10) (d) (10, 4)
  21. 21.What is the distance between the points (1, 6) and (9, 12)? (a) 10 (b) 100 (c) 14 (d) 11
  22. 22.In which quadrant does the point (−3, 5) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  23. 23.What is the distance between the points (1, 6) and (9, 0)? (a) 14 (b) 10 (c) 100 (d) 11
  24. 24.What is the midpoint of the line joining (4, 8) and (12, 16)? (a) (16, 24) (b) (12, 8) (c) (8, 12) (d) (4, 4)
  25. 25.In which quadrant does the point (−7, −3) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  26. 26.In which quadrant does the point (−1, 7) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  27. 27.What is the distance between the points (2, 2) and (10, 17)? (a) 17 (b) 23 (c) 18 (d) 289
  28. 28.In which quadrant does the point (2, 5) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
  29. 29.How far is the point (8, 6) from the origin (0, 0)? (a) 10 (b) 100 (c) 11 (d) 14
  30. 30.In which quadrant does the point (8, 7) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  31. 31.What is the distance between the points (4, 8) and (16, 13)? (a) 17 (b) 13 (c) 14 (d) 169
  32. 32.What is the midpoint of the line joining (0, 2) and (12, 6)? (a) (4, 6) (b) (6, 4) (c) (6, 2) (d) (12, 8)
  33. 33.How far is the point (8, 15) from the origin (0, 0)? (a) 18 (b) 289 (c) 17 (d) 23
  34. 34.What is the distance between the points (7, 6) and (10, 2)? (a) 5 (b) 6 (c) 25 (d) 7
  35. 35.What is the midpoint of the line joining (9, 12) and (15, 0)? (a) (6, 12) (b) (12, 6) (c) (24, 12) (d) (3, 6)
  36. 36.What is the midpoint of the line joining (8, 3) and (10, 13)? (a) (1, 5) (b) (18, 16) (c) (9, 8) (d) (8, 9)
  37. 37.What is the midpoint of the line joining (10, 14) and (16, 6)? (a) (10, 13) (b) (26, 20) (c) (3, 4) (d) (13, 10)
  38. 38.What is the midpoint of the line joining (1, 11) and (3, 1)? (a) (4, 12) (b) (2, 6) (c) (6, 2) (d) (1, 5)
  39. 39.In which quadrant does the point (−3, 1) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  40. 40.What is the distance between the points (6, 12) and (12, 4)? (a) 11 (b) 100 (c) 10 (d) 14

Answer key

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

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