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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 278 · 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 (2, 10) and (12, 0)? (a) (5, 5) (b) (14, 10) (c) (7, 5) (d) (5, 7)
  2. 2.How far is the point (3, 4) from the origin (0, 0)? (a) 5 (b) 6 (c) 25 (d) 7
  3. 3.What is the midpoint of the line joining (9, 8) and (19, 2)? (a) (28, 10) (b) (5, 3) (c) (14, 5) (d) (5, 14)
  4. 4.How far is the point (5, 12) from the origin (0, 0)? (a) 14 (b) 169 (c) 13 (d) 17
  5. 5.What is the midpoint of the line joining (10, 2) and (22, 4)? (a) (32, 6) (b) (6, 1) (c) (16, 3) (d) (3, 16)
  6. 6.In which quadrant does the point (1, 8) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  7. 7.What is the distance between the points (7, 12) and (31, 5)? (a) 31 (b) 26 (c) 25 (d) 625
  8. 8.In which quadrant does the point (−6, 7) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  9. 9.What is the distance between the points (4, 16) and (28, 9)? (a) 26 (b) 625 (c) 31 (d) 25
  10. 10.What is the distance between the points (7, 18) and (19, 2)? (a) 21 (b) 20 (c) 28 (d) 400
  11. 11.What is the distance between the points (8, 8) and (16, 23)? (a) 23 (b) 18 (c) 17 (d) 289
  12. 12.How far is the point (9, 12) from the origin (0, 0)? (a) 21 (b) 15 (c) 16 (d) 225
  13. 13.How far is the point (12, 9) from the origin (0, 0)? (a) 225 (b) 16 (c) 21 (d) 15
  14. 14.What is the distance between the points (9, 9) and (21, 18)? (a) 225 (b) 16 (c) 21 (d) 15
  15. 15.What is the distance between the points (1, 8) and (16, 16)? (a) 17 (b) 18 (c) 289 (d) 23
  16. 16.How far is the point (24, 7) from the origin (0, 0)? (a) 625 (b) 25 (c) 31 (d) 26
  17. 17.In which quadrant does the point (−3, 1) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  18. 18.In which quadrant does the point (9, 8) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  19. 19.How far is the point (15, 8) from the origin (0, 0)? (a) 18 (b) 289 (c) 23 (d) 17
  20. 20.In which quadrant does the point (−9, 4) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  21. 21.In which quadrant does the point (−3, −6) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  22. 22.What is the midpoint of the line joining (5, 8) and (17, 2)? (a) (6, 3) (b) (22, 10) (c) (5, 11) (d) (11, 5)
  23. 23.What is the distance between the points (2, 6) and (8, 14)? (a) 100 (b) 14 (c) 11 (d) 10
  24. 24.In which quadrant does the point (−5, 1) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  25. 25.How far is the point (6, 8) from the origin (0, 0)? (a) 10 (b) 100 (c) 14 (d) 11
  26. 26.What is the midpoint of the line joining (0, 0) and (12, 2)? (a) (7, 1) (b) (12, 2) (c) (6, 1) (d) (1, 6)
  27. 27.In which quadrant does the point (−5, 7) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  28. 28.In which quadrant does the point (−1, −8) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  29. 29.In which quadrant does the point (1, 3) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  30. 30.What is the distance between the points (4, 9) and (19, 17)? (a) 23 (b) 17 (c) 289 (d) 18
  31. 31.What is the distance between the points (5, 1) and (17, 17)? (a) 20 (b) 400 (c) 28 (d) 21
  32. 32.What is the midpoint of the line joining (1, 1) and (7, 9)? (a) (4, 5) (b) (3, 4) (c) (5, 4) (d) (8, 10)
  33. 33.How far is the point (8, 6) from the origin (0, 0)? (a) 10 (b) 14 (c) 11 (d) 100
  34. 34.What is the midpoint of the line joining (10, 3) and (18, 15)? (a) (14, 9) (b) (9, 14) (c) (4, 6) (d) (28, 18)
  35. 35.What is the midpoint of the line joining (5, 10) and (9, 18)? (a) (14, 7) (b) (7, 14) (c) (2, 4) (d) (14, 28)
  36. 36.In which quadrant does the point (−2, 7) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  37. 37.In which quadrant does the point (−1, −5) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  38. 38.What is the midpoint of the line joining (2, 8) and (6, 6)? (a) (8, 14) (b) (4, 7) (c) (7, 4) (d) (2, 1)
  39. 39.In which quadrant does the point (7, 6) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  40. 40.What is the distance between the points (1, 7) and (17, 19)? (a) 28 (b) 20 (c) 21 (d) 400

Answer key

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

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