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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 422 · 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 distance between the points (4, 5) and (20, 17)? (a) 400 (b) 28 (c) 21 (d) 20
  2. 2.What is the midpoint of the line joining (4, 8) and (12, 20)? (a) (4, 6) (b) (16, 28) (c) (14, 8) (d) (8, 14)
  3. 3.What is the distance between the points (8, 5) and (11, 1)? (a) 7 (b) 6 (c) 25 (d) 5
  4. 4.What is the distance between the points (8, 13) and (13, 1)? (a) 14 (b) 169 (c) 17 (d) 13
  5. 5.What is the distance between the points (9, 12) and (17, 6)? (a) 100 (b) 14 (c) 10 (d) 11
  6. 6.In which quadrant does the point (2, 1) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  7. 7.How far is the point (16, 12) from the origin (0, 0)? (a) 20 (b) 28 (c) 21 (d) 400
  8. 8.What is the midpoint of the line joining (6, 2) and (18, 0)? (a) (12, 1) (b) (24, 2) (c) (1, 12) (d) (6, 1)
  9. 9.What is the distance between the points (8, 2) and (20, 11)? (a) 15 (b) 225 (c) 16 (d) 21
  10. 10.In which quadrant does the point (6, −6) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  11. 11.What is the distance between the points (0, 3) and (12, 19)? (a) 400 (b) 21 (c) 28 (d) 20
  12. 12.What is the distance between the points (0, 8) and (4, 11)? (a) 7 (b) 25 (c) 5 (d) 6
  13. 13.What is the distance between the points (4, 1) and (7, 5)? (a) 25 (b) 7 (c) 5 (d) 6
  14. 14.What is the midpoint of the line joining (7, 2) and (9, 10)? (a) (8, 6) (b) (1, 4) (c) (6, 8) (d) (16, 12)
  15. 15.How far is the point (8, 6) from the origin (0, 0)? (a) 11 (b) 10 (c) 100 (d) 14
  16. 16.How far is the point (4, 3) from the origin (0, 0)? (a) 25 (b) 5 (c) 6 (d) 7
  17. 17.How far is the point (8, 15) from the origin (0, 0)? (a) 17 (b) 18 (c) 289 (d) 23
  18. 18.What is the midpoint of the line joining (10, 7) and (18, 19)? (a) (28, 26) (b) (4, 6) (c) (14, 13) (d) (13, 14)
  19. 19.What is the midpoint of the line joining (8, 17) and (10, 7)? (a) (9, 12) (b) (18, 24) (c) (12, 9) (d) (1, 5)
  20. 20.What is the midpoint of the line joining (6, 4) and (16, 2)? (a) (5, 1) (b) (22, 6) (c) (11, 3) (d) (3, 11)
  21. 21.What is the midpoint of the line joining (3, 6) and (13, 12)? (a) (5, 3) (b) (9, 8) (c) (16, 18) (d) (8, 9)
  22. 22.What is the distance between the points (7, 20) and (12, 8)? (a) 13 (b) 169 (c) 17 (d) 14
  23. 23.What is the distance between the points (7, 6) and (13, 14)? (a) 10 (b) 100 (c) 11 (d) 14
  24. 24.What is the midpoint of the line joining (10, 2) and (12, 12)? (a) (1, 5) (b) (7, 11) (c) (11, 7) (d) (22, 14)
  25. 25.What is the distance between the points (0, 12) and (6, 4)? (a) 100 (b) 10 (c) 11 (d) 14
  26. 26.In which quadrant does the point (−3, −9) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  27. 27.In which quadrant does the point (9, 6) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  28. 28.In which quadrant does the point (9, −8) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  29. 29.What is the midpoint of the line joining (3, 16) and (9, 4)? (a) (10, 6) (b) (12, 20) (c) (3, 6) (d) (6, 10)
  30. 30.In which quadrant does the point (−8, 3) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  31. 31.How far is the point (15, 8) from the origin (0, 0)? (a) 289 (b) 23 (c) 17 (d) 18
  32. 32.What is the distance between the points (0, 8) and (8, 14)? (a) 11 (b) 100 (c) 14 (d) 10
  33. 33.How far is the point (12, 9) from the origin (0, 0)? (a) 15 (b) 225 (c) 21 (d) 16
  34. 34.What is the distance between the points (7, 14) and (13, 6)? (a) 11 (b) 14 (c) 10 (d) 100
  35. 35.What is the midpoint of the line joining (3, 5) and (13, 7)? (a) (6, 8) (b) (16, 12) (c) (8, 6) (d) (5, 1)
  36. 36.What is the midpoint of the line joining (1, 8) and (3, 14)? (a) (2, 11) (b) (1, 3) (c) (11, 2) (d) (4, 22)
  37. 37.What is the distance between the points (2, 13) and (7, 1)? (a) 17 (b) 13 (c) 14 (d) 169
  38. 38.What is the midpoint of the line joining (0, 17) and (2, 5)? (a) (1, 11) (b) (2, 22) (c) (1, 6) (d) (11, 1)
  39. 39.What is the distance between the points (3, 29) and (10, 5)? (a) 625 (b) 25 (c) 31 (d) 26
  40. 40.How far is the point (24, 7) from the origin (0, 0)? (a) 25 (b) 625 (c) 31 (d) 26

Answer key

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

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