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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 652 · 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 (1, 4) and (3, 0)? (a) (1, 2) (b) (2, 2) (c) (4, 4) (d) (3, 2)
  2. 2.In which quadrant does the point (−5, −3) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  3. 3.In which quadrant does the point (−2, 5) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  4. 4.What is the midpoint of the line joining (3, 9) and (13, 7)? (a) (8, 8) (b) (16, 16) (c) (9, 8) (d) (5, 1)
  5. 5.What is the midpoint of the line joining (9, 6) and (11, 0)? (a) (1, 3) (b) (10, 3) (c) (20, 6) (d) (3, 10)
  6. 6.In which quadrant does the point (3, −6) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  7. 7.What is the midpoint of the line joining (3, 5) and (7, 9)? (a) (10, 14) (b) (7, 5) (c) (2, 2) (d) (5, 7)
  8. 8.What is the midpoint of the line joining (1, 8) and (3, 20)? (a) (1, 6) (b) (4, 28) (c) (14, 2) (d) (2, 14)
  9. 9.In which quadrant does the point (−7, 2) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  10. 10.What is the midpoint of the line joining (3, 12) and (9, 6)? (a) (3, 3) (b) (12, 18) (c) (9, 6) (d) (6, 9)
  11. 11.What is the distance between the points (1, 9) and (13, 25)? (a) 20 (b) 28 (c) 400 (d) 21
  12. 12.What is the distance between the points (3, 2) and (18, 10)? (a) 289 (b) 17 (c) 23 (d) 18
  13. 13.What is the distance between the points (9, 6) and (17, 12)? (a) 10 (b) 100 (c) 14 (d) 11
  14. 14.What is the distance between the points (6, 17) and (22, 5)? (a) 28 (b) 20 (c) 21 (d) 400
  15. 15.What is the distance between the points (6, 2) and (9, 6)? (a) 6 (b) 7 (c) 25 (d) 5
  16. 16.How far is the point (8, 15) from the origin (0, 0)? (a) 23 (b) 289 (c) 17 (d) 18
  17. 17.What is the midpoint of the line joining (4, 7) and (10, 13)? (a) (10, 7) (b) (7, 10) (c) (14, 20) (d) (3, 3)
  18. 18.How far is the point (6, 8) from the origin (0, 0)? (a) 14 (b) 10 (c) 100 (d) 11
  19. 19.What is the distance between the points (6, 26) and (13, 2)? (a) 625 (b) 31 (c) 26 (d) 25
  20. 20.What is the distance between the points (8, 0) and (14, 8)? (a) 14 (b) 100 (c) 11 (d) 10
  21. 21.What is the distance between the points (1, 17) and (13, 8)? (a) 16 (b) 15 (c) 225 (d) 21
  22. 22.How far is the point (24, 7) from the origin (0, 0)? (a) 625 (b) 25 (c) 26 (d) 31
  23. 23.What is the distance between the points (4, 9) and (28, 16)? (a) 625 (b) 31 (c) 26 (d) 25
  24. 24.How far is the point (12, 5) from the origin (0, 0)? (a) 17 (b) 14 (c) 169 (d) 13
  25. 25.What is the distance between the points (4, 8) and (8, 11)? (a) 25 (b) 5 (c) 7 (d) 6
  26. 26.What is the midpoint of the line joining (1, 0) and (11, 10)? (a) (5, 6) (b) (5, 5) (c) (6, 5) (d) (12, 10)
  27. 27.In which quadrant does the point (−2, −9) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  28. 28.What is the distance between the points (9, 8) and (12, 4)? (a) 6 (b) 25 (c) 5 (d) 7
  29. 29.What is the distance between the points (5, 5) and (17, 0)? (a) 169 (b) 13 (c) 17 (d) 14
  30. 30.How far is the point (5, 12) from the origin (0, 0)? (a) 14 (b) 13 (c) 17 (d) 169
  31. 31.What is the distance between the points (5, 29) and (12, 5)? (a) 31 (b) 625 (c) 26 (d) 25
  32. 32.In which quadrant does the point (−6, 2) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  33. 33.What is the distance between the points (9, 5) and (17, 11)? (a) 14 (b) 10 (c) 11 (d) 100
  34. 34.What is the distance between the points (1, 15) and (25, 8)? (a) 25 (b) 26 (c) 625 (d) 31
  35. 35.In which quadrant does the point (7, 6) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  36. 36.How far is the point (8, 6) from the origin (0, 0)? (a) 100 (b) 14 (c) 11 (d) 10
  37. 37.How far is the point (12, 16) from the origin (0, 0)? (a) 20 (b) 400 (c) 21 (d) 28
  38. 38.What is the midpoint of the line joining (2, 1) and (12, 3)? (a) (14, 4) (b) (5, 1) (c) (7, 2) (d) (2, 7)
  39. 39.What is the distance between the points (7, 1) and (10, 5)? (a) 25 (b) 5 (c) 7 (d) 6
  40. 40.How far is the point (3, 4) from the origin (0, 0)? (a) 7 (b) 5 (c) 25 (d) 6

Answer key

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

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