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Coordinate Geometry Worksheet for Maths Olympiad

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

Answer key

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

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