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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 88 · 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.How far is the point (8, 15) from the origin (0, 0)? (a) 18 (b) 17 (c) 289 (d) 23
  2. 2.What is the distance between the points (2, 6) and (9, 30)? (a) 31 (b) 26 (c) 25 (d) 625
  3. 3.What is the midpoint of the line joining (8, 2) and (12, 8)? (a) (5, 10) (b) (2, 3) (c) (10, 5) (d) (20, 10)
  4. 4.What is the midpoint of the line joining (2, 0) and (6, 2)? (a) (1, 4) (b) (4, 1) (c) (2, 1) (d) (8, 2)
  5. 5.What is the midpoint of the line joining (9, 10) and (21, 0)? (a) (15, 5) (b) (5, 15) (c) (30, 10) (d) (6, 5)
  6. 6.In which quadrant does the point (4, −3) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  7. 7.How far is the point (9, 12) from the origin (0, 0)? (a) 15 (b) 16 (c) 225 (d) 21
  8. 8.What is the midpoint of the line joining (1, 19) and (3, 9)? (a) (1, 5) (b) (14, 2) (c) (2, 14) (d) (4, 28)
  9. 9.What is the midpoint of the line joining (10, 0) and (16, 6)? (a) (13, 3) (b) (3, 13) (c) (26, 6) (d) (3, 3)
  10. 10.How far is the point (12, 9) from the origin (0, 0)? (a) 21 (b) 16 (c) 225 (d) 15
  11. 11.What is the distance between the points (5, 11) and (9, 8)? (a) 25 (b) 5 (c) 7 (d) 6
  12. 12.How far is the point (8, 6) from the origin (0, 0)? (a) 100 (b) 11 (c) 10 (d) 14
  13. 13.What is the distance between the points (1, 18) and (10, 6)? (a) 16 (b) 21 (c) 225 (d) 15
  14. 14.How far is the point (16, 12) from the origin (0, 0)? (a) 28 (b) 21 (c) 20 (d) 400
  15. 15.What is the midpoint of the line joining (0, 14) and (4, 10)? (a) (12, 2) (b) (4, 24) (c) (2, 2) (d) (2, 12)
  16. 16.What is the distance between the points (1, 3) and (4, 7)? (a) 7 (b) 5 (c) 25 (d) 6
  17. 17.What is the distance between the points (0, 18) and (12, 9)? (a) 15 (b) 16 (c) 225 (d) 21
  18. 18.What is the midpoint of the line joining (9, 14) and (11, 8)? (a) (11, 10) (b) (20, 22) (c) (1, 3) (d) (10, 11)
  19. 19.What is the distance between the points (1, 13) and (7, 5)? (a) 10 (b) 14 (c) 100 (d) 11
  20. 20.What is the distance between the points (1, 25) and (13, 9)? (a) 20 (b) 28 (c) 400 (d) 21
  21. 21.What is the distance between the points (2, 0) and (17, 8)? (a) 289 (b) 23 (c) 18 (d) 17
  22. 22.How far is the point (5, 12) from the origin (0, 0)? (a) 17 (b) 14 (c) 169 (d) 13
  23. 23.What is the midpoint of the line joining (4, 11) and (12, 3)? (a) (8, 7) (b) (4, 4) (c) (16, 14) (d) (7, 8)
  24. 24.In which quadrant does the point (7, −9) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  25. 25.In which quadrant does the point (3, 4) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  26. 26.In which quadrant does the point (−8, −2) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
  27. 27.What is the midpoint of the line joining (6, 0) and (10, 12)? (a) (16, 12) (b) (6, 8) (c) (2, 6) (d) (8, 6)
  28. 28.How far is the point (6, 8) from the origin (0, 0)? (a) 10 (b) 14 (c) 100 (d) 11
  29. 29.In which quadrant does the point (6, 9) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  30. 30.What is the distance between the points (8, 24) and (16, 9)? (a) 17 (b) 18 (c) 23 (d) 289
  31. 31.What is the midpoint of the line joining (7, 15) and (11, 3)? (a) (18, 18) (b) (2, 6) (c) (9, 9) (d) (10, 9)
  32. 32.How far is the point (7, 24) from the origin (0, 0)? (a) 625 (b) 26 (c) 31 (d) 25
  33. 33.What is the distance between the points (7, 2) and (19, 7)? (a) 14 (b) 169 (c) 17 (d) 13
  34. 34.What is the midpoint of the line joining (9, 5) and (11, 11)? (a) (8, 10) (b) (20, 16) (c) (1, 3) (d) (10, 8)
  35. 35.What is the midpoint of the line joining (3, 7) and (7, 11)? (a) (9, 5) (b) (2, 2) (c) (5, 9) (d) (10, 18)
  36. 36.What is the distance between the points (5, 1) and (11, 9)? (a) 14 (b) 11 (c) 10 (d) 100
  37. 37.What is the midpoint of the line joining (4, 7) and (14, 15)? (a) (9, 11) (b) (11, 9) (c) (5, 4) (d) (18, 22)
  38. 38.What is the distance between the points (1, 9) and (10, 21)? (a) 225 (b) 21 (c) 16 (d) 15
  39. 39.In which quadrant does the point (2, 2) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  40. 40.What is the distance between the points (3, 15) and (12, 3)? (a) 225 (b) 15 (c) 21 (d) 16

Answer key

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

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