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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 210 · 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 (1, 8) and (7, 0)? (a) 100 (b) 11 (c) 14 (d) 10
  2. 2.What is the distance between the points (6, 6) and (9, 2)? (a) 25 (b) 5 (c) 6 (d) 7
  3. 3.What is the distance between the points (5, 7) and (11, 15)? (a) 100 (b) 14 (c) 11 (d) 10
  4. 4.How far is the point (6, 8) from the origin (0, 0)? (a) 11 (b) 100 (c) 14 (d) 10
  5. 5.What is the midpoint of the line joining (7, 7) and (15, 9)? (a) (8, 11) (b) (22, 16) (c) (4, 1) (d) (11, 8)
  6. 6.How far is the point (12, 5) from the origin (0, 0)? (a) 17 (b) 13 (c) 14 (d) 169
  7. 7.What is the distance between the points (0, 3) and (8, 9)? (a) 14 (b) 10 (c) 100 (d) 11
  8. 8.What is the midpoint of the line joining (5, 13) and (9, 1)? (a) (14, 14) (b) (2, 6) (c) (8, 7) (d) (7, 7)
  9. 9.In which quadrant does the point (−4, 2) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  10. 10.How far is the point (8, 6) from the origin (0, 0)? (a) 10 (b) 100 (c) 11 (d) 14
  11. 11.How far is the point (15, 8) from the origin (0, 0)? (a) 18 (b) 289 (c) 17 (d) 23
  12. 12.In which quadrant does the point (2, 4) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  13. 13.In which quadrant does the point (7, −5) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  14. 14.What is the distance between the points (2, 8) and (5, 4)? (a) 7 (b) 6 (c) 5 (d) 25
  15. 15.What is the distance between the points (1, 25) and (8, 1)? (a) 625 (b) 26 (c) 25 (d) 31
  16. 16.What is the midpoint of the line joining (5, 14) and (9, 8)? (a) (2, 3) (b) (11, 7) (c) (7, 11) (d) (14, 22)
  17. 17.What is the midpoint of the line joining (9, 8) and (11, 20)? (a) (14, 10) (b) (1, 6) (c) (10, 14) (d) (20, 28)
  18. 18.How far is the point (16, 12) from the origin (0, 0)? (a) 400 (b) 28 (c) 21 (d) 20
  19. 19.In which quadrant does the point (9, 2) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  20. 20.How far is the point (12, 16) from the origin (0, 0)? (a) 28 (b) 400 (c) 21 (d) 20
  21. 21.In which quadrant does the point (−5, 4) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  22. 22.What is the midpoint of the line joining (5, 4) and (13, 10)? (a) (7, 9) (b) (4, 3) (c) (18, 14) (d) (9, 7)
  23. 23.In which quadrant does the point (7, 1) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  24. 24.What is the distance between the points (0, 6) and (4, 9)? (a) 7 (b) 6 (c) 5 (d) 25
  25. 25.How far is the point (24, 7) from the origin (0, 0)? (a) 625 (b) 31 (c) 26 (d) 25
  26. 26.What is the distance between the points (3, 8) and (12, 20)? (a) 21 (b) 225 (c) 16 (d) 15
  27. 27.What is the midpoint of the line joining (10, 4) and (14, 8)? (a) (6, 12) (b) (12, 6) (c) (24, 12) (d) (2, 2)
  28. 28.What is the distance between the points (1, 19) and (9, 4)? (a) 289 (b) 23 (c) 18 (d) 17
  29. 29.What is the distance between the points (6, 9) and (13, 33)? (a) 31 (b) 625 (c) 26 (d) 25
  30. 30.In which quadrant does the point (−1, 7) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
  31. 31.What is the distance between the points (5, 2) and (13, 8)? (a) 10 (b) 100 (c) 11 (d) 14
  32. 32.In which quadrant does the point (4, −6) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  33. 33.What is the midpoint of the line joining (7, 7) and (9, 9)? (a) (1, 1) (b) (8, 8) (c) (9, 8) (d) (16, 16)
  34. 34.How far is the point (4, 3) from the origin (0, 0)? (a) 5 (b) 25 (c) 7 (d) 6
  35. 35.In which quadrant does the point (−6, 2) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  36. 36.In which quadrant does the point (3, 1) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  37. 37.What is the distance between the points (9, 4) and (13, 7)? (a) 25 (b) 7 (c) 6 (d) 5
  38. 38.What is the distance between the points (2, 18) and (11, 6)? (a) 225 (b) 16 (c) 15 (d) 21
  39. 39.What is the midpoint of the line joining (3, 11) and (15, 9)? (a) (6, 1) (b) (10, 9) (c) (18, 20) (d) (9, 10)
  40. 40.What is the midpoint of the line joining (0, 4) and (8, 2)? (a) (3, 4) (b) (8, 6) (c) (4, 3) (d) (4, 1)

Answer key

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

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