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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 752 · 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 (1, 5) and (13, 10)? (a) 17 (b) 13 (c) 169 (d) 14
  2. 2.How far is the point (16, 12) from the origin (0, 0)? (a) 21 (b) 28 (c) 400 (d) 20
  3. 3.What is the distance between the points (5, 4) and (14, 16)? (a) 21 (b) 225 (c) 16 (d) 15
  4. 4.How far is the point (12, 9) from the origin (0, 0)? (a) 16 (b) 225 (c) 21 (d) 15
  5. 5.In which quadrant does the point (9, 4) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  6. 6.What is the midpoint of the line joining (9, 16) and (15, 10)? (a) (12, 13) (b) (24, 26) (c) (13, 12) (d) (3, 3)
  7. 7.What is the distance between the points (9, 9) and (18, 21)? (a) 21 (b) 225 (c) 15 (d) 16
  8. 8.In which quadrant does the point (−7, −9) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  9. 9.What is the distance between the points (0, 2) and (9, 14)? (a) 225 (b) 21 (c) 15 (d) 16
  10. 10.How far is the point (8, 6) from the origin (0, 0)? (a) 100 (b) 14 (c) 11 (d) 10
  11. 11.How far is the point (5, 12) from the origin (0, 0)? (a) 14 (b) 17 (c) 169 (d) 13
  12. 12.What is the distance between the points (0, 5) and (8, 11)? (a) 14 (b) 100 (c) 10 (d) 11
  13. 13.What is the midpoint of the line joining (10, 13) and (20, 3)? (a) (8, 15) (b) (15, 8) (c) (5, 5) (d) (30, 16)
  14. 14.In which quadrant does the point (3, 8) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  15. 15.How far is the point (4, 3) from the origin (0, 0)? (a) 5 (b) 25 (c) 7 (d) 6
  16. 16.How far is the point (3, 4) from the origin (0, 0)? (a) 25 (b) 6 (c) 5 (d) 7
  17. 17.What is the midpoint of the line joining (5, 2) and (13, 4)? (a) (9, 3) (b) (18, 6) (c) (3, 9) (d) (4, 1)
  18. 18.In which quadrant does the point (−4, 2) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  19. 19.What is the distance between the points (6, 8) and (12, 0)? (a) 14 (b) 11 (c) 10 (d) 100
  20. 20.What is the distance between the points (2, 5) and (9, 29)? (a) 25 (b) 31 (c) 26 (d) 625
  21. 21.What is the midpoint of the line joining (9, 5) and (17, 7)? (a) (26, 12) (b) (6, 13) (c) (13, 6) (d) (4, 1)
  22. 22.What is the distance between the points (9, 0) and (21, 5)? (a) 13 (b) 169 (c) 17 (d) 14
  23. 23.What is the midpoint of the line joining (0, 8) and (4, 12)? (a) (10, 2) (b) (2, 10) (c) (4, 20) (d) (2, 2)
  24. 24.What is the distance between the points (1, 8) and (13, 24)? (a) 21 (b) 28 (c) 20 (d) 400
  25. 25.What is the distance between the points (1, 9) and (9, 15)? (a) 100 (b) 11 (c) 14 (d) 10
  26. 26.What is the distance between the points (1, 4) and (17, 16)? (a) 28 (b) 20 (c) 21 (d) 400
  27. 27.What is the midpoint of the line joining (8, 10) and (12, 16)? (a) (2, 3) (b) (20, 26) (c) (13, 10) (d) (10, 13)
  28. 28.What is the distance between the points (0, 2) and (4, 5)? (a) 7 (b) 25 (c) 6 (d) 5
  29. 29.What is the distance between the points (8, 0) and (23, 8)? (a) 23 (b) 289 (c) 17 (d) 18
  30. 30.What is the midpoint of the line joining (3, 10) and (7, 16)? (a) (10, 26) (b) (5, 13) (c) (13, 5) (d) (2, 3)
  31. 31.What is the distance between the points (2, 2) and (14, 18)? (a) 21 (b) 28 (c) 400 (d) 20
  32. 32.What is the distance between the points (8, 2) and (24, 14)? (a) 21 (b) 400 (c) 20 (d) 28
  33. 33.What is the distance between the points (7, 18) and (19, 2)? (a) 400 (b) 28 (c) 21 (d) 20
  34. 34.What is the distance between the points (9, 2) and (25, 14)? (a) 400 (b) 28 (c) 21 (d) 20
  35. 35.What is the midpoint of the line joining (0, 9) and (10, 15)? (a) (5, 3) (b) (5, 12) (c) (12, 5) (d) (10, 24)
  36. 36.How far is the point (12, 16) from the origin (0, 0)? (a) 21 (b) 20 (c) 28 (d) 400
  37. 37.What is the distance between the points (0, 12) and (8, 6)? (a) 11 (b) 14 (c) 10 (d) 100
  38. 38.What is the distance between the points (8, 11) and (11, 7)? (a) 25 (b) 6 (c) 5 (d) 7
  39. 39.How far is the point (6, 8) from the origin (0, 0)? (a) 10 (b) 11 (c) 100 (d) 14
  40. 40.What is the distance between the points (3, 14) and (9, 6)? (a) 14 (b) 10 (c) 100 (d) 11

Answer key

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

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