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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 990 · 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 (0, 4) and (9, 16)? (a) 16 (b) 15 (c) 21 (d) 225
  2. 2.How far is the point (6, 8) from the origin (0, 0)? (a) 10 (b) 100 (c) 14 (d) 11
  3. 3.What is the midpoint of the line joining (10, 0) and (22, 4)? (a) (2, 16) (b) (32, 4) (c) (16, 2) (d) (6, 2)
  4. 4.What is the distance between the points (9, 15) and (18, 3)? (a) 21 (b) 225 (c) 16 (d) 15
  5. 5.In which quadrant does the point (3, 7) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  6. 6.How far is the point (5, 12) from the origin (0, 0)? (a) 17 (b) 169 (c) 14 (d) 13
  7. 7.How far is the point (12, 16) from the origin (0, 0)? (a) 400 (b) 28 (c) 21 (d) 20
  8. 8.How far is the point (4, 3) from the origin (0, 0)? (a) 6 (b) 25 (c) 5 (d) 7
  9. 9.In which quadrant does the point (2, −1) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  10. 10.In which quadrant does the point (9, 2) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  11. 11.What is the midpoint of the line joining (9, 10) and (21, 0)? (a) (5, 15) (b) (6, 5) (c) (30, 10) (d) (15, 5)
  12. 12.What is the distance between the points (4, 2) and (16, 18)? (a) 21 (b) 400 (c) 28 (d) 20
  13. 13.What is the midpoint of the line joining (2, 6) and (14, 8)? (a) (16, 14) (b) (6, 1) (c) (7, 8) (d) (8, 7)
  14. 14.What is the distance between the points (9, 13) and (14, 1)? (a) 14 (b) 13 (c) 17 (d) 169
  15. 15.How far is the point (7, 24) from the origin (0, 0)? (a) 25 (b) 26 (c) 31 (d) 625
  16. 16.What is the distance between the points (3, 4) and (7, 1)? (a) 6 (b) 25 (c) 5 (d) 7
  17. 17.What is the distance between the points (5, 17) and (17, 8)? (a) 21 (b) 16 (c) 225 (d) 15
  18. 18.What is the distance between the points (0, 14) and (15, 6)? (a) 23 (b) 289 (c) 18 (d) 17
  19. 19.In which quadrant does the point (−1, −2) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  20. 20.What is the midpoint of the line joining (9, 1) and (17, 13)? (a) (4, 6) (b) (7, 13) (c) (13, 7) (d) (26, 14)
  21. 21.How far is the point (3, 4) from the origin (0, 0)? (a) 6 (b) 7 (c) 25 (d) 5
  22. 22.What is the distance between the points (5, 6) and (29, 13)? (a) 26 (b) 25 (c) 31 (d) 625
  23. 23.How far is the point (9, 12) from the origin (0, 0)? (a) 21 (b) 15 (c) 225 (d) 16
  24. 24.What is the distance between the points (0, 18) and (16, 6)? (a) 28 (b) 21 (c) 400 (d) 20
  25. 25.What is the midpoint of the line joining (10, 5) and (12, 11)? (a) (8, 11) (b) (22, 16) (c) (11, 8) (d) (1, 3)
  26. 26.What is the midpoint of the line joining (9, 9) and (19, 13)? (a) (28, 22) (b) (14, 11) (c) (11, 14) (d) (5, 2)
  27. 27.In which quadrant does the point (−6, 6) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  28. 28.What is the distance between the points (5, 5) and (8, 1)? (a) 6 (b) 7 (c) 25 (d) 5
  29. 29.What is the midpoint of the line joining (6, 2) and (12, 4)? (a) (18, 6) (b) (3, 1) (c) (9, 3) (d) (3, 9)
  30. 30.What is the distance between the points (4, 10) and (16, 5)? (a) 169 (b) 17 (c) 14 (d) 13
  31. 31.In which quadrant does the point (−6, −3) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
  32. 32.In which quadrant does the point (−2, 9) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  33. 33.What is the distance between the points (6, 14) and (18, 5)? (a) 225 (b) 21 (c) 16 (d) 15
  34. 34.What is the distance between the points (7, 10) and (19, 5)? (a) 17 (b) 169 (c) 14 (d) 13
  35. 35.What is the midpoint of the line joining (3, 4) and (13, 14)? (a) (9, 8) (b) (5, 5) (c) (8, 9) (d) (16, 18)
  36. 36.What is the distance between the points (3, 22) and (15, 6)? (a) 20 (b) 400 (c) 21 (d) 28
  37. 37.What is the distance between the points (0, 13) and (3, 9)? (a) 25 (b) 7 (c) 6 (d) 5
  38. 38.How far is the point (8, 6) from the origin (0, 0)? (a) 14 (b) 100 (c) 10 (d) 11
  39. 39.In which quadrant does the point (−6, −9) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  40. 40.What is the distance between the points (5, 17) and (11, 9)? (a) 10 (b) 14 (c) 11 (d) 100

Answer key

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

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