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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 479 · 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, 13) and (14, 1)? (a) (12, 7) (b) (2, 6) (c) (7, 12) (d) (24, 14)
  2. 2.What is the midpoint of the line joining (0, 16) and (10, 8)? (a) (12, 5) (b) (5, 4) (c) (5, 12) (d) (10, 24)
  3. 3.What is the midpoint of the line joining (0, 3) and (2, 13)? (a) (1, 5) (b) (1, 8) (c) (8, 1) (d) (2, 16)
  4. 4.What is the midpoint of the line joining (9, 7) and (19, 11)? (a) (5, 2) (b) (14, 9) (c) (9, 14) (d) (28, 18)
  5. 5.How far is the point (9, 12) from the origin (0, 0)? (a) 16 (b) 21 (c) 225 (d) 15
  6. 6.In which quadrant does the point (−1, −8) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  7. 7.What is the distance between the points (2, 3) and (14, 8)? (a) 17 (b) 14 (c) 169 (d) 13
  8. 8.What is the midpoint of the line joining (2, 8) and (8, 6)? (a) (5, 7) (b) (10, 14) (c) (7, 5) (d) (3, 1)
  9. 9.What is the distance between the points (6, 2) and (13, 26)? (a) 625 (b) 31 (c) 26 (d) 25
  10. 10.How far is the point (4, 3) from the origin (0, 0)? (a) 25 (b) 7 (c) 6 (d) 5
  11. 11.How far is the point (6, 8) from the origin (0, 0)? (a) 100 (b) 10 (c) 11 (d) 14
  12. 12.What is the distance between the points (9, 8) and (12, 12)? (a) 5 (b) 7 (c) 6 (d) 25
  13. 13.What is the distance between the points (5, 1) and (17, 17)? (a) 28 (b) 21 (c) 20 (d) 400
  14. 14.What is the distance between the points (5, 12) and (14, 0)? (a) 15 (b) 225 (c) 16 (d) 21
  15. 15.What is the distance between the points (8, 4) and (11, 0)? (a) 6 (b) 5 (c) 7 (d) 25
  16. 16.What is the midpoint of the line joining (10, 13) and (14, 5)? (a) (24, 18) (b) (9, 12) (c) (2, 4) (d) (12, 9)
  17. 17.What is the distance between the points (4, 20) and (20, 8)? (a) 20 (b) 21 (c) 28 (d) 400
  18. 18.How far is the point (24, 7) from the origin (0, 0)? (a) 31 (b) 25 (c) 26 (d) 625
  19. 19.What is the distance between the points (0, 15) and (15, 7)? (a) 18 (b) 23 (c) 17 (d) 289
  20. 20.In which quadrant does the point (−8, −2) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  21. 21.In which quadrant does the point (−5, −6) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  22. 22.In which quadrant does the point (2, 3) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  23. 23.How far is the point (12, 5) from the origin (0, 0)? (a) 13 (b) 14 (c) 17 (d) 169
  24. 24.In which quadrant does the point (−1, −1) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  25. 25.What is the distance between the points (2, 6) and (18, 18)? (a) 21 (b) 400 (c) 28 (d) 20
  26. 26.In which quadrant does the point (−9, −7) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  27. 27.In which quadrant does the point (−7, −8) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  28. 28.What is the distance between the points (7, 9) and (22, 17)? (a) 17 (b) 18 (c) 289 (d) 23
  29. 29.What is the midpoint of the line joining (2, 0) and (4, 6)? (a) (1, 3) (b) (4, 3) (c) (3, 3) (d) (6, 6)
  30. 30.What is the distance between the points (6, 3) and (22, 15)? (a) 400 (b) 21 (c) 28 (d) 20
  31. 31.What is the midpoint of the line joining (6, 13) and (18, 3)? (a) (24, 16) (b) (12, 8) (c) (8, 12) (d) (6, 5)
  32. 32.How far is the point (16, 12) from the origin (0, 0)? (a) 400 (b) 20 (c) 21 (d) 28
  33. 33.What is the midpoint of the line joining (4, 10) and (12, 22)? (a) (4, 6) (b) (16, 8) (c) (16, 32) (d) (8, 16)
  34. 34.How far is the point (5, 12) from the origin (0, 0)? (a) 169 (b) 13 (c) 14 (d) 17
  35. 35.What is the distance between the points (8, 7) and (16, 22)? (a) 289 (b) 23 (c) 17 (d) 18
  36. 36.What is the distance between the points (3, 7) and (11, 22)? (a) 17 (b) 23 (c) 289 (d) 18
  37. 37.What is the distance between the points (9, 13) and (25, 1)? (a) 20 (b) 400 (c) 28 (d) 21
  38. 38.What is the distance between the points (0, 12) and (8, 6)? (a) 100 (b) 10 (c) 11 (d) 14
  39. 39.What is the distance between the points (0, 4) and (5, 16)? (a) 169 (b) 17 (c) 14 (d) 13
  40. 40.How far is the point (7, 24) from the origin (0, 0)? (a) 31 (b) 625 (c) 26 (d) 25

Answer key

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

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