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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 175 · 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 (12, 16) from the origin (0, 0)? (a) 28 (b) 21 (c) 400 (d) 20
  2. 2.What is the distance between the points (0, 1) and (12, 17)? (a) 28 (b) 21 (c) 400 (d) 20
  3. 3.What is the midpoint of the line joining (1, 17) and (13, 9)? (a) (6, 4) (b) (7, 13) (c) (14, 26) (d) (13, 7)
  4. 4.What is the distance between the points (4, 8) and (16, 13)? (a) 169 (b) 17 (c) 14 (d) 13
  5. 5.What is the distance between the points (4, 6) and (13, 18)? (a) 21 (b) 15 (c) 225 (d) 16
  6. 6.What is the distance between the points (5, 1) and (13, 7)? (a) 14 (b) 11 (c) 100 (d) 10
  7. 7.What is the midpoint of the line joining (5, 4) and (11, 2)? (a) (3, 1) (b) (16, 6) (c) (3, 8) (d) (8, 3)
  8. 8.What is the midpoint of the line joining (9, 2) and (11, 6)? (a) (10, 4) (b) (20, 8) (c) (4, 10) (d) (1, 2)
  9. 9.In which quadrant does the point (−5, −1) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  10. 10.What is the midpoint of the line joining (4, 4) and (12, 6)? (a) (16, 10) (b) (8, 5) (c) (5, 8) (d) (4, 1)
  11. 11.What is the distance between the points (9, 7) and (21, 2)? (a) 13 (b) 169 (c) 17 (d) 14
  12. 12.What is the distance between the points (4, 30) and (11, 6)? (a) 31 (b) 25 (c) 625 (d) 26
  13. 13.What is the distance between the points (6, 2) and (22, 14)? (a) 21 (b) 20 (c) 28 (d) 400
  14. 14.In which quadrant does the point (−1, 5) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  15. 15.In which quadrant does the point (4, 3) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  16. 16.What is the midpoint of the line joining (0, 19) and (6, 7)? (a) (13, 3) (b) (3, 6) (c) (6, 26) (d) (3, 13)
  17. 17.How far is the point (3, 4) from the origin (0, 0)? (a) 25 (b) 6 (c) 7 (d) 5
  18. 18.What is the midpoint of the line joining (2, 13) and (14, 3)? (a) (6, 5) (b) (16, 16) (c) (8, 8) (d) (9, 8)
  19. 19.What is the distance between the points (3, 9) and (27, 2)? (a) 625 (b) 25 (c) 31 (d) 26
  20. 20.What is the distance between the points (0, 0) and (7, 24)? (a) 26 (b) 625 (c) 31 (d) 25
  21. 21.How far is the point (7, 24) from the origin (0, 0)? (a) 625 (b) 25 (c) 26 (d) 31
  22. 22.How far is the point (15, 8) from the origin (0, 0)? (a) 289 (b) 17 (c) 23 (d) 18
  23. 23.In which quadrant does the point (3, 3) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  24. 24.What is the midpoint of the line joining (9, 18) and (17, 10)? (a) (14, 13) (b) (4, 4) (c) (26, 28) (d) (13, 14)
  25. 25.What is the distance between the points (7, 18) and (19, 2)? (a) 28 (b) 400 (c) 20 (d) 21
  26. 26.What is the midpoint of the line joining (1, 9) and (13, 13)? (a) (6, 2) (b) (7, 11) (c) (14, 22) (d) (11, 7)
  27. 27.In which quadrant does the point (9, −7) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  28. 28.What is the distance between the points (9, 13) and (25, 1)? (a) 400 (b) 21 (c) 20 (d) 28
  29. 29.What is the midpoint of the line joining (1, 13) and (7, 7)? (a) (10, 4) (b) (4, 10) (c) (3, 3) (d) (8, 20)
  30. 30.What is the distance between the points (4, 5) and (12, 20)? (a) 289 (b) 18 (c) 17 (d) 23
  31. 31.What is the midpoint of the line joining (7, 0) and (9, 12)? (a) (1, 6) (b) (16, 12) (c) (6, 8) (d) (8, 6)
  32. 32.What is the distance between the points (2, 14) and (14, 9)? (a) 17 (b) 169 (c) 13 (d) 14
  33. 33.What is the distance between the points (5, 13) and (14, 1)? (a) 225 (b) 21 (c) 16 (d) 15
  34. 34.What is the distance between the points (9, 15) and (15, 7)? (a) 14 (b) 11 (c) 10 (d) 100
  35. 35.How far is the point (6, 8) from the origin (0, 0)? (a) 10 (b) 14 (c) 11 (d) 100
  36. 36.How far is the point (5, 12) from the origin (0, 0)? (a) 13 (b) 169 (c) 17 (d) 14
  37. 37.In which quadrant does the point (1, −6) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  38. 38.How far is the point (8, 6) from the origin (0, 0)? (a) 14 (b) 100 (c) 11 (d) 10
  39. 39.What is the distance between the points (7, 1) and (31, 8)? (a) 625 (b) 31 (c) 26 (d) 25
  40. 40.In which quadrant does the point (−6, −1) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant

Answer key

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

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