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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 233 · 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 (10, 18) and (22, 8)? (a) (16, 13) (b) (13, 16) (c) (32, 26) (d) (6, 5)
  2. 2.How far is the point (5, 12) from the origin (0, 0)? (a) 169 (b) 17 (c) 13 (d) 14
  3. 3.What is the distance between the points (2, 5) and (18, 17)? (a) 21 (b) 20 (c) 400 (d) 28
  4. 4.What is the distance between the points (0, 6) and (8, 21)? (a) 17 (b) 23 (c) 289 (d) 18
  5. 5.What is the distance between the points (8, 13) and (24, 1)? (a) 400 (b) 21 (c) 20 (d) 28
  6. 6.What is the midpoint of the line joining (8, 12) and (18, 0)? (a) (26, 12) (b) (6, 13) (c) (5, 6) (d) (13, 6)
  7. 7.What is the distance between the points (7, 23) and (19, 7)? (a) 400 (b) 21 (c) 28 (d) 20
  8. 8.What is the midpoint of the line joining (4, 10) and (6, 18)? (a) (14, 5) (b) (10, 28) (c) (5, 14) (d) (1, 4)
  9. 9.How far is the point (8, 15) from the origin (0, 0)? (a) 17 (b) 289 (c) 23 (d) 18
  10. 10.What is the distance between the points (9, 8) and (24, 16)? (a) 289 (b) 23 (c) 18 (d) 17
  11. 11.What is the midpoint of the line joining (8, 10) and (14, 12)? (a) (22, 22) (b) (3, 1) (c) (11, 11) (d) (12, 11)
  12. 12.What is the midpoint of the line joining (4, 1) and (8, 9)? (a) (2, 4) (b) (12, 10) (c) (6, 5) (d) (5, 6)
  13. 13.How far is the point (12, 9) from the origin (0, 0)? (a) 15 (b) 21 (c) 16 (d) 225
  14. 14.What is the distance between the points (3, 9) and (9, 17)? (a) 10 (b) 14 (c) 11 (d) 100
  15. 15.In which quadrant does the point (−7, −5) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  16. 16.What is the distance between the points (9, 19) and (18, 7)? (a) 16 (b) 15 (c) 225 (d) 21
  17. 17.What is the midpoint of the line joining (2, 7) and (4, 1)? (a) (3, 4) (b) (1, 3) (c) (6, 8) (d) (4, 3)
  18. 18.What is the distance between the points (1, 24) and (8, 0)? (a) 625 (b) 26 (c) 25 (d) 31
  19. 19.In which quadrant does the point (−7, 2) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  20. 20.What is the distance between the points (6, 7) and (9, 3)? (a) 25 (b) 7 (c) 6 (d) 5
  21. 21.How far is the point (3, 4) from the origin (0, 0)? (a) 25 (b) 7 (c) 5 (d) 6
  22. 22.What is the distance between the points (0, 14) and (9, 2)? (a) 15 (b) 21 (c) 225 (d) 16
  23. 23.How far is the point (6, 8) from the origin (0, 0)? (a) 10 (b) 14 (c) 11 (d) 100
  24. 24.How far is the point (4, 3) from the origin (0, 0)? (a) 25 (b) 5 (c) 7 (d) 6
  25. 25.What is the midpoint of the line joining (6, 13) and (18, 7)? (a) (12, 10) (b) (24, 20) (c) (6, 3) (d) (10, 12)
  26. 26.How far is the point (12, 5) from the origin (0, 0)? (a) 169 (b) 13 (c) 17 (d) 14
  27. 27.How far is the point (15, 8) from the origin (0, 0)? (a) 23 (b) 17 (c) 18 (d) 289
  28. 28.In which quadrant does the point (1, −2) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  29. 29.What is the midpoint of the line joining (4, 0) and (16, 2)? (a) (1, 10) (b) (20, 2) (c) (6, 1) (d) (10, 1)
  30. 30.What is the midpoint of the line joining (10, 6) and (18, 16)? (a) (11, 14) (b) (4, 5) (c) (14, 11) (d) (28, 22)
  31. 31.What is the distance between the points (1, 0) and (9, 6)? (a) 10 (b) 11 (c) 100 (d) 14
  32. 32.In which quadrant does the point (−8, 9) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  33. 33.What is the distance between the points (3, 6) and (19, 18)? (a) 21 (b) 20 (c) 400 (d) 28
  34. 34.In which quadrant does the point (−4, 2) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  35. 35.What is the distance between the points (1, 1) and (8, 25)? (a) 625 (b) 31 (c) 25 (d) 26
  36. 36.In which quadrant does the point (−3, 1) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  37. 37.In which quadrant does the point (3, 4) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  38. 38.In which quadrant does the point (−1, −7) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  39. 39.In which quadrant does the point (2, −7) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
  40. 40.What is the midpoint of the line joining (1, 8) and (9, 6)? (a) (10, 14) (b) (4, 1) (c) (7, 5) (d) (5, 7)

Answer key

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

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