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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 359 · 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 midpoint of the line joining (0, 1) and (8, 9)? (a) (4, 4) (b) (8, 10) (c) (4, 5) (d) (5, 4)
  2. 2.In which quadrant does the point (5, 1) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  3. 3.What is the midpoint of the line joining (4, 0) and (8, 4)? (a) (2, 2) (b) (2, 6) (c) (12, 4) (d) (6, 2)
  4. 4.What is the distance between the points (9, 8) and (12, 12)? (a) 25 (b) 5 (c) 6 (d) 7
  5. 5.In which quadrant does the point (9, 2) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  6. 6.How far is the point (12, 5) from the origin (0, 0)? (a) 169 (b) 14 (c) 17 (d) 13
  7. 7.How far is the point (5, 12) from the origin (0, 0)? (a) 14 (b) 13 (c) 169 (d) 17
  8. 8.What is the distance between the points (2, 0) and (14, 9)? (a) 16 (b) 15 (c) 225 (d) 21
  9. 9.In which quadrant does the point (6, −1) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  10. 10.In which quadrant does the point (4, 6) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  11. 11.What is the midpoint of the line joining (8, 3) and (18, 15)? (a) (9, 13) (b) (5, 6) (c) (26, 18) (d) (13, 9)
  12. 12.What is the distance between the points (7, 5) and (22, 13)? (a) 18 (b) 23 (c) 289 (d) 17
  13. 13.What is the distance between the points (9, 8) and (15, 16)? (a) 100 (b) 14 (c) 10 (d) 11
  14. 14.What is the distance between the points (9, 0) and (33, 7)? (a) 26 (b) 625 (c) 25 (d) 31
  15. 15.What is the midpoint of the line joining (7, 14) and (19, 2)? (a) (6, 6) (b) (8, 13) (c) (26, 16) (d) (13, 8)
  16. 16.How far is the point (24, 7) from the origin (0, 0)? (a) 26 (b) 31 (c) 625 (d) 25
  17. 17.What is the midpoint of the line joining (4, 17) and (8, 7)? (a) (12, 24) (b) (12, 6) (c) (2, 5) (d) (6, 12)
  18. 18.What is the midpoint of the line joining (8, 2) and (16, 6)? (a) (24, 8) (b) (4, 12) (c) (4, 2) (d) (12, 4)
  19. 19.What is the midpoint of the line joining (6, 1) and (10, 5)? (a) (8, 3) (b) (2, 2) (c) (16, 6) (d) (3, 8)
  20. 20.What is the midpoint of the line joining (10, 2) and (12, 10)? (a) (6, 11) (b) (22, 12) (c) (1, 4) (d) (11, 6)
  21. 21.How far is the point (6, 8) from the origin (0, 0)? (a) 11 (b) 10 (c) 100 (d) 14
  22. 22.What is the midpoint of the line joining (0, 4) and (2, 8)? (a) (6, 1) (b) (2, 12) (c) (1, 2) (d) (1, 6)
  23. 23.What is the distance between the points (7, 7) and (11, 10)? (a) 6 (b) 7 (c) 5 (d) 25
  24. 24.What is the distance between the points (1, 8) and (7, 0)? (a) 14 (b) 10 (c) 11 (d) 100
  25. 25.In which quadrant does the point (7, −2) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  26. 26.In which quadrant does the point (9, 8) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  27. 27.What is the distance between the points (5, 1) and (14, 13)? (a) 225 (b) 15 (c) 21 (d) 16
  28. 28.How far is the point (9, 12) from the origin (0, 0)? (a) 225 (b) 16 (c) 21 (d) 15
  29. 29.What is the midpoint of the line joining (6, 6) and (14, 14)? (a) (11, 10) (b) (10, 10) (c) (4, 4) (d) (20, 20)
  30. 30.In which quadrant does the point (−9, 6) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  31. 31.How far is the point (3, 4) from the origin (0, 0)? (a) 5 (b) 6 (c) 25 (d) 7
  32. 32.What is the distance between the points (1, 25) and (13, 9)? (a) 400 (b) 28 (c) 20 (d) 21
  33. 33.What is the distance between the points (3, 2) and (11, 17)? (a) 18 (b) 289 (c) 17 (d) 23
  34. 34.What is the midpoint of the line joining (0, 5) and (6, 1)? (a) (6, 6) (b) (3, 3) (c) (4, 3) (d) (3, 2)
  35. 35.How far is the point (16, 12) from the origin (0, 0)? (a) 28 (b) 400 (c) 21 (d) 20
  36. 36.What is the distance between the points (0, 16) and (16, 4)? (a) 21 (b) 28 (c) 400 (d) 20
  37. 37.What is the distance between the points (5, 13) and (29, 6)? (a) 31 (b) 625 (c) 25 (d) 26
  38. 38.What is the distance between the points (1, 9) and (17, 21)? (a) 20 (b) 400 (c) 21 (d) 28
  39. 39.What is the midpoint of the line joining (9, 18) and (17, 8)? (a) (4, 5) (b) (14, 13) (c) (26, 26) (d) (13, 13)
  40. 40.What is the midpoint of the line joining (0, 2) and (4, 6)? (a) (2, 2) (b) (4, 8) (c) (4, 2) (d) (2, 4)

Answer key

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

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