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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 979 · 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 (4, −2) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  2. 2.What is the distance between the points (0, 0) and (12, 16)? (a) 20 (b) 400 (c) 21 (d) 28
  3. 3.What is the midpoint of the line joining (0, 8) and (2, 6)? (a) (2, 14) (b) (7, 1) (c) (1, 1) (d) (1, 7)
  4. 4.What is the midpoint of the line joining (5, 5) and (9, 7)? (a) (2, 1) (b) (6, 7) (c) (7, 6) (d) (14, 12)
  5. 5.How far is the point (12, 16) from the origin (0, 0)? (a) 21 (b) 400 (c) 28 (d) 20
  6. 6.In which quadrant does the point (9, −6) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  7. 7.What is the midpoint of the line joining (9, 10) and (13, 4)? (a) (2, 3) (b) (7, 11) (c) (22, 14) (d) (11, 7)
  8. 8.How far is the point (4, 3) from the origin (0, 0)? (a) 25 (b) 5 (c) 7 (d) 6
  9. 9.What is the distance between the points (1, 1) and (13, 17)? (a) 28 (b) 400 (c) 21 (d) 20
  10. 10.In which quadrant does the point (−7, −3) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  11. 11.What is the midpoint of the line joining (8, 5) and (10, 17)? (a) (1, 6) (b) (11, 9) (c) (18, 22) (d) (9, 11)
  12. 12.What is the midpoint of the line joining (0, 2) and (12, 12)? (a) (6, 7) (b) (6, 5) (c) (12, 14) (d) (7, 6)
  13. 13.What is the distance between the points (3, 24) and (10, 0)? (a) 26 (b) 31 (c) 625 (d) 25
  14. 14.What is the midpoint of the line joining (1, 20) and (3, 10)? (a) (1, 5) (b) (2, 15) (c) (15, 2) (d) (4, 30)
  15. 15.What is the midpoint of the line joining (1, 9) and (11, 7)? (a) (6, 8) (b) (12, 16) (c) (8, 6) (d) (5, 1)
  16. 16.How far is the point (16, 12) from the origin (0, 0)? (a) 20 (b) 21 (c) 28 (d) 400
  17. 17.What is the distance between the points (1, 5) and (5, 2)? (a) 25 (b) 5 (c) 7 (d) 6
  18. 18.What is the distance between the points (4, 6) and (9, 18)? (a) 169 (b) 17 (c) 14 (d) 13
  19. 19.What is the midpoint of the line joining (8, 10) and (16, 14)? (a) (4, 2) (b) (24, 24) (c) (12, 12) (d) (13, 12)
  20. 20.What is the distance between the points (8, 0) and (11, 4)? (a) 6 (b) 5 (c) 7 (d) 25
  21. 21.What is the midpoint of the line joining (3, 9) and (5, 3)? (a) (1, 3) (b) (6, 4) (c) (4, 6) (d) (8, 12)
  22. 22.How far is the point (3, 4) from the origin (0, 0)? (a) 6 (b) 25 (c) 5 (d) 7
  23. 23.What is the distance between the points (2, 13) and (10, 7)? (a) 11 (b) 100 (c) 10 (d) 14
  24. 24.What is the midpoint of the line joining (1, 16) and (3, 4)? (a) (4, 20) (b) (1, 6) (c) (2, 10) (d) (10, 2)
  25. 25.How far is the point (8, 6) from the origin (0, 0)? (a) 100 (b) 11 (c) 14 (d) 10
  26. 26.What is the distance between the points (1, 5) and (4, 9)? (a) 7 (b) 25 (c) 5 (d) 6
  27. 27.What is the distance between the points (3, 21) and (11, 6)? (a) 17 (b) 18 (c) 23 (d) 289
  28. 28.What is the midpoint of the line joining (0, 9) and (10, 1)? (a) (6, 5) (b) (5, 4) (c) (10, 10) (d) (5, 5)
  29. 29.In which quadrant does the point (3, −9) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  30. 30.What is the distance between the points (9, 18) and (21, 2)? (a) 28 (b) 400 (c) 20 (d) 21
  31. 31.What is the midpoint of the line joining (8, 9) and (14, 7)? (a) (11, 8) (b) (8, 11) (c) (22, 16) (d) (3, 1)
  32. 32.What is the distance between the points (9, 9) and (21, 25)? (a) 28 (b) 400 (c) 20 (d) 21
  33. 33.What is the distance between the points (2, 25) and (9, 1)? (a) 26 (b) 625 (c) 31 (d) 25
  34. 34.What is the midpoint of the line joining (5, 7) and (11, 5)? (a) (3, 1) (b) (16, 12) (c) (8, 6) (d) (6, 8)
  35. 35.What is the distance between the points (2, 2) and (11, 14)? (a) 16 (b) 225 (c) 15 (d) 21
  36. 36.How far is the point (9, 12) from the origin (0, 0)? (a) 225 (b) 21 (c) 15 (d) 16
  37. 37.In which quadrant does the point (−7, 3) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  38. 38.In which quadrant does the point (−1, −7) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  39. 39.What is the distance between the points (8, 9) and (23, 1)? (a) 17 (b) 289 (c) 18 (d) 23
  40. 40.What is the distance between the points (5, 16) and (20, 8)? (a) 17 (b) 289 (c) 18 (d) 23

Answer key

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

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