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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 837 · 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, 4) and (18, 13)? (a) 21 (b) 225 (c) 15 (d) 16
  2. 2.In which quadrant does the point (3, 5) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
  3. 3.What is the midpoint of the line joining (2, 2) and (12, 10)? (a) (14, 12) (b) (7, 6) (c) (5, 4) (d) (6, 7)
  4. 4.What is the distance between the points (4, 9) and (7, 5)? (a) 5 (b) 7 (c) 6 (d) 25
  5. 5.What is the distance between the points (9, 3) and (21, 19)? (a) 20 (b) 21 (c) 28 (d) 400
  6. 6.In which quadrant does the point (−5, 6) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  7. 7.In which quadrant does the point (−3, −3) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  8. 8.What is the midpoint of the line joining (7, 8) and (13, 10)? (a) (9, 10) (b) (20, 18) (c) (3, 1) (d) (10, 9)
  9. 9.What is the midpoint of the line joining (6, 14) and (10, 6)? (a) (8, 10) (b) (2, 4) (c) (16, 20) (d) (10, 8)
  10. 10.What is the distance between the points (6, 2) and (22, 14)? (a) 21 (b) 20 (c) 28 (d) 400
  11. 11.In which quadrant does the point (6, 8) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  12. 12.How far is the point (8, 15) from the origin (0, 0)? (a) 23 (b) 17 (c) 18 (d) 289
  13. 13.In which quadrant does the point (4, 9) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  14. 14.How far is the point (5, 12) from the origin (0, 0)? (a) 169 (b) 13 (c) 17 (d) 14
  15. 15.How far is the point (9, 12) from the origin (0, 0)? (a) 225 (b) 21 (c) 15 (d) 16
  16. 16.What is the distance between the points (1, 5) and (9, 20)? (a) 23 (b) 17 (c) 289 (d) 18
  17. 17.What is the distance between the points (0, 7) and (8, 1)? (a) 10 (b) 11 (c) 14 (d) 100
  18. 18.How far is the point (3, 4) from the origin (0, 0)? (a) 7 (b) 25 (c) 5 (d) 6
  19. 19.What is the midpoint of the line joining (3, 3) and (13, 7)? (a) (5, 2) (b) (16, 10) (c) (5, 8) (d) (8, 5)
  20. 20.What is the distance between the points (3, 2) and (12, 14)? (a) 15 (b) 225 (c) 16 (d) 21
  21. 21.What is the midpoint of the line joining (7, 5) and (19, 11)? (a) (6, 3) (b) (8, 13) (c) (26, 16) (d) (13, 8)
  22. 22.How far is the point (24, 7) from the origin (0, 0)? (a) 625 (b) 31 (c) 26 (d) 25
  23. 23.What is the midpoint of the line joining (6, 10) and (14, 4)? (a) (4, 3) (b) (20, 14) (c) (7, 10) (d) (10, 7)
  24. 24.What is the midpoint of the line joining (4, 2) and (6, 14)? (a) (8, 5) (b) (10, 16) (c) (1, 6) (d) (5, 8)
  25. 25.What is the distance between the points (0, 0) and (4, 3)? (a) 6 (b) 7 (c) 5 (d) 25
  26. 26.What is the midpoint of the line joining (6, 1) and (8, 11)? (a) (14, 12) (b) (6, 7) (c) (7, 6) (d) (1, 5)
  27. 27.What is the midpoint of the line joining (10, 8) and (16, 10)? (a) (13, 9) (b) (26, 18) (c) (3, 1) (d) (9, 13)
  28. 28.What is the midpoint of the line joining (7, 7) and (15, 5)? (a) (22, 12) (b) (4, 1) (c) (11, 6) (d) (6, 11)
  29. 29.In which quadrant does the point (−1, 1) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  30. 30.What is the midpoint of the line joining (4, 8) and (16, 18)? (a) (20, 26) (b) (13, 10) (c) (6, 5) (d) (10, 13)
  31. 31.What is the midpoint of the line joining (1, 8) and (11, 20)? (a) (6, 14) (b) (5, 6) (c) (12, 28) (d) (14, 6)
  32. 32.In which quadrant does the point (−2, 8) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  33. 33.What is the distance between the points (3, 24) and (15, 8)? (a) 21 (b) 20 (c) 400 (d) 28
  34. 34.What is the distance between the points (0, 3) and (4, 0)? (a) 5 (b) 7 (c) 6 (d) 25
  35. 35.What is the midpoint of the line joining (3, 9) and (13, 21)? (a) (15, 8) (b) (8, 15) (c) (5, 6) (d) (16, 30)
  36. 36.In which quadrant does the point (−3, 7) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  37. 37.What is the distance between the points (4, 20) and (20, 8)? (a) 28 (b) 21 (c) 400 (d) 20
  38. 38.What is the distance between the points (9, 5) and (14, 17)? (a) 17 (b) 169 (c) 14 (d) 13
  39. 39.In which quadrant does the point (4, −8) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  40. 40.What is the distance between the points (6, 9) and (9, 5)? (a) 25 (b) 7 (c) 6 (d) 5

Answer key

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

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