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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 368 · 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 (6, 8) and (18, 17)? (a) 225 (b) 15 (c) 21 (d) 16
  2. 2.What is the midpoint of the line joining (3, 10) and (9, 20)? (a) (15, 6) (b) (3, 5) (c) (6, 15) (d) (12, 30)
  3. 3.How far is the point (5, 12) from the origin (0, 0)? (a) 169 (b) 14 (c) 17 (d) 13
  4. 4.What is the midpoint of the line joining (5, 7) and (15, 19)? (a) (13, 10) (b) (5, 6) (c) (20, 26) (d) (10, 13)
  5. 5.What is the distance between the points (4, 7) and (20, 19)? (a) 21 (b) 400 (c) 20 (d) 28
  6. 6.How far is the point (15, 8) from the origin (0, 0)? (a) 289 (b) 17 (c) 23 (d) 18
  7. 7.What is the midpoint of the line joining (10, 14) and (18, 2)? (a) (28, 16) (b) (4, 6) (c) (8, 14) (d) (14, 8)
  8. 8.How far is the point (3, 4) from the origin (0, 0)? (a) 25 (b) 5 (c) 6 (d) 7
  9. 9.How far is the point (16, 12) from the origin (0, 0)? (a) 20 (b) 21 (c) 400 (d) 28
  10. 10.How far is the point (9, 12) from the origin (0, 0)? (a) 21 (b) 225 (c) 15 (d) 16
  11. 11.What is the distance between the points (9, 8) and (33, 1)? (a) 25 (b) 625 (c) 26 (d) 31
  12. 12.How far is the point (12, 5) from the origin (0, 0)? (a) 13 (b) 17 (c) 169 (d) 14
  13. 13.In which quadrant does the point (−5, 7) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  14. 14.What is the distance between the points (1, 14) and (7, 6)? (a) 100 (b) 14 (c) 10 (d) 11
  15. 15.What is the distance between the points (4, 3) and (11, 27)? (a) 625 (b) 25 (c) 31 (d) 26
  16. 16.What is the distance between the points (8, 5) and (12, 8)? (a) 25 (b) 7 (c) 5 (d) 6
  17. 17.What is the midpoint of the line joining (9, 9) and (13, 17)? (a) (22, 26) (b) (2, 4) (c) (13, 11) (d) (11, 13)
  18. 18.What is the midpoint of the line joining (9, 1) and (13, 13)? (a) (11, 7) (b) (7, 11) (c) (22, 14) (d) (2, 6)
  19. 19.How far is the point (8, 15) from the origin (0, 0)? (a) 289 (b) 23 (c) 17 (d) 18
  20. 20.How far is the point (12, 9) from the origin (0, 0)? (a) 15 (b) 16 (c) 225 (d) 21
  21. 21.How far is the point (4, 3) from the origin (0, 0)? (a) 7 (b) 6 (c) 25 (d) 5
  22. 22.What is the distance between the points (9, 2) and (21, 11)? (a) 15 (b) 21 (c) 16 (d) 225
  23. 23.What is the distance between the points (4, 17) and (19, 9)? (a) 23 (b) 289 (c) 18 (d) 17
  24. 24.What is the distance between the points (7, 9) and (14, 33)? (a) 26 (b) 625 (c) 31 (d) 25
  25. 25.In which quadrant does the point (−6, 8) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  26. 26.What is the midpoint of the line joining (4, 7) and (6, 13)? (a) (10, 20) (b) (5, 10) (c) (1, 3) (d) (10, 5)
  27. 27.How far is the point (24, 7) from the origin (0, 0)? (a) 26 (b) 625 (c) 25 (d) 31
  28. 28.In which quadrant does the point (−1, −6) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  29. 29.In which quadrant does the point (−7, 3) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  30. 30.What is the midpoint of the line joining (8, 2) and (20, 6)? (a) (4, 14) (b) (14, 4) (c) (28, 8) (d) (6, 2)
  31. 31.What is the midpoint of the line joining (2, 10) and (4, 2)? (a) (6, 12) (b) (6, 3) (c) (1, 4) (d) (3, 6)
  32. 32.In which quadrant does the point (4, 6) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  33. 33.What is the distance between the points (9, 12) and (21, 3)? (a) 21 (b) 225 (c) 16 (d) 15
  34. 34.In which quadrant does the point (−9, 8) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  35. 35.What is the midpoint of the line joining (7, 7) and (19, 11)? (a) (26, 18) (b) (6, 2) (c) (9, 13) (d) (13, 9)
  36. 36.What is the midpoint of the line joining (5, 10) and (7, 14)? (a) (12, 6) (b) (12, 24) (c) (1, 2) (d) (6, 12)
  37. 37.In which quadrant does the point (8, 8) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  38. 38.What is the midpoint of the line joining (5, 8) and (17, 18)? (a) (11, 13) (b) (22, 26) (c) (13, 11) (d) (6, 5)
  39. 39.What is the midpoint of the line joining (6, 10) and (10, 4)? (a) (16, 14) (b) (2, 3) (c) (7, 8) (d) (8, 7)
  40. 40.What is the midpoint of the line joining (1, 15) and (5, 9)? (a) (2, 3) (b) (12, 3) (c) (3, 12) (d) (6, 24)

Answer key

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

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