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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 384 · 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 (7, 17) and (23, 5)? (a) 21 (b) 28 (c) 20 (d) 400
  2. 2.What is the distance between the points (5, 8) and (20, 0)? (a) 17 (b) 23 (c) 18 (d) 289
  3. 3.What is the distance between the points (5, 3) and (17, 19)? (a) 21 (b) 28 (c) 400 (d) 20
  4. 4.What is the midpoint of the line joining (0, 1) and (10, 13)? (a) (5, 6) (b) (5, 7) (c) (7, 5) (d) (10, 14)
  5. 5.What is the distance between the points (3, 2) and (15, 11)? (a) 15 (b) 16 (c) 225 (d) 21
  6. 6.How far is the point (8, 6) from the origin (0, 0)? (a) 100 (b) 14 (c) 10 (d) 11
  7. 7.What is the midpoint of the line joining (4, 15) and (14, 9)? (a) (9, 12) (b) (18, 24) (c) (12, 9) (d) (5, 3)
  8. 8.What is the distance between the points (4, 2) and (28, 9)? (a) 625 (b) 31 (c) 26 (d) 25
  9. 9.What is the midpoint of the line joining (4, 9) and (16, 21)? (a) (15, 10) (b) (20, 30) (c) (10, 15) (d) (6, 6)
  10. 10.How far is the point (6, 8) from the origin (0, 0)? (a) 100 (b) 14 (c) 10 (d) 11
  11. 11.In which quadrant does the point (1, −2) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  12. 12.What is the midpoint of the line joining (9, 14) and (21, 4)? (a) (9, 15) (b) (15, 9) (c) (6, 5) (d) (30, 18)
  13. 13.In which quadrant does the point (−9, 7) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  14. 14.What is the midpoint of the line joining (8, 3) and (10, 7)? (a) (9, 5) (b) (18, 10) (c) (5, 9) (d) (1, 2)
  15. 15.What is the midpoint of the line joining (2, 19) and (4, 7)? (a) (6, 26) (b) (1, 6) (c) (13, 3) (d) (3, 13)
  16. 16.How far is the point (12, 5) from the origin (0, 0)? (a) 17 (b) 169 (c) 14 (d) 13
  17. 17.How far is the point (12, 9) from the origin (0, 0)? (a) 21 (b) 16 (c) 15 (d) 225
  18. 18.What is the midpoint of the line joining (5, 2) and (11, 14)? (a) (16, 16) (b) (9, 8) (c) (3, 6) (d) (8, 8)
  19. 19.What is the midpoint of the line joining (3, 13) and (15, 1)? (a) (9, 7) (b) (18, 14) (c) (7, 9) (d) (6, 6)
  20. 20.What is the midpoint of the line joining (8, 13) and (16, 1)? (a) (4, 6) (b) (12, 7) (c) (7, 12) (d) (24, 14)
  21. 21.What is the distance between the points (4, 14) and (19, 6)? (a) 17 (b) 18 (c) 23 (d) 289
  22. 22.What is the distance between the points (8, 2) and (16, 8)? (a) 10 (b) 100 (c) 11 (d) 14
  23. 23.What is the distance between the points (5, 4) and (17, 20)? (a) 400 (b) 28 (c) 21 (d) 20
  24. 24.In which quadrant does the point (7, 1) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  25. 25.In which quadrant does the point (−4, 4) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  26. 26.What is the distance between the points (6, 3) and (9, 7)? (a) 5 (b) 6 (c) 7 (d) 25
  27. 27.How far is the point (5, 12) from the origin (0, 0)? (a) 169 (b) 13 (c) 14 (d) 17
  28. 28.What is the distance between the points (6, 7) and (21, 15)? (a) 18 (b) 23 (c) 289 (d) 17
  29. 29.What is the distance between the points (4, 9) and (12, 24)? (a) 23 (b) 289 (c) 17 (d) 18
  30. 30.What is the midpoint of the line joining (1, 2) and (13, 14)? (a) (14, 16) (b) (8, 7) (c) (6, 6) (d) (7, 8)
  31. 31.What is the midpoint of the line joining (4, 14) and (14, 6)? (a) (9, 10) (b) (18, 20) (c) (10, 9) (d) (5, 4)
  32. 32.What is the distance between the points (0, 12) and (9, 0)? (a) 21 (b) 16 (c) 15 (d) 225
  33. 33.What is the distance between the points (1, 6) and (9, 21)? (a) 18 (b) 23 (c) 17 (d) 289
  34. 34.What is the midpoint of the line joining (8, 8) and (16, 4)? (a) (6, 12) (b) (12, 6) (c) (24, 12) (d) (4, 2)
  35. 35.How far is the point (24, 7) from the origin (0, 0)? (a) 26 (b) 25 (c) 625 (d) 31
  36. 36.What is the distance between the points (5, 7) and (11, 15)? (a) 100 (b) 11 (c) 10 (d) 14
  37. 37.What is the midpoint of the line joining (2, 0) and (6, 2)? (a) (8, 2) (b) (1, 4) (c) (2, 1) (d) (4, 1)
  38. 38.In which quadrant does the point (5, 5) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  39. 39.In which quadrant does the point (−3, −3) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  40. 40.What is the midpoint of the line joining (0, 10) and (4, 16)? (a) (13, 2) (b) (2, 13) (c) (4, 26) (d) (2, 3)

Answer key

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

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