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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 481 · 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.In which quadrant does the point (−2, −7) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  2. 2.What is the midpoint of the line joining (5, 12) and (7, 10)? (a) (11, 6) (b) (1, 1) (c) (6, 11) (d) (12, 22)
  3. 3.In which quadrant does the point (−1, 2) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  4. 4.In which quadrant does the point (6, 5) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  5. 5.What is the distance between the points (7, 3) and (31, 10)? (a) 26 (b) 31 (c) 25 (d) 625
  6. 6.In which quadrant does the point (−6, −3) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  7. 7.What is the midpoint of the line joining (2, 10) and (6, 14)? (a) (4, 12) (b) (8, 24) (c) (12, 4) (d) (2, 2)
  8. 8.What is the midpoint of the line joining (1, 8) and (9, 12)? (a) (4, 2) (b) (10, 20) (c) (5, 10) (d) (10, 5)
  9. 9.What is the midpoint of the line joining (1, 17) and (9, 9)? (a) (5, 13) (b) (13, 5) (c) (10, 26) (d) (4, 4)
  10. 10.In which quadrant does the point (6, 2) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  11. 11.What is the distance between the points (9, 24) and (16, 0)? (a) 26 (b) 625 (c) 31 (d) 25
  12. 12.What is the distance between the points (7, 9) and (12, 21)? (a) 13 (b) 17 (c) 14 (d) 169
  13. 13.What is the distance between the points (4, 21) and (12, 6)? (a) 17 (b) 23 (c) 289 (d) 18
  14. 14.What is the midpoint of the line joining (2, 10) and (4, 16)? (a) (13, 3) (b) (3, 13) (c) (1, 3) (d) (6, 26)
  15. 15.How far is the point (3, 4) from the origin (0, 0)? (a) 5 (b) 6 (c) 7 (d) 25
  16. 16.What is the distance between the points (6, 13) and (15, 1)? (a) 15 (b) 225 (c) 16 (d) 21
  17. 17.In which quadrant does the point (−1, 1) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  18. 18.What is the distance between the points (5, 0) and (13, 6)? (a) 14 (b) 100 (c) 11 (d) 10
  19. 19.What is the midpoint of the line joining (8, 7) and (12, 1)? (a) (2, 3) (b) (10, 4) (c) (20, 8) (d) (4, 10)
  20. 20.What is the distance between the points (0, 12) and (15, 4)? (a) 23 (b) 18 (c) 289 (d) 17
  21. 21.How far is the point (16, 12) from the origin (0, 0)? (a) 20 (b) 21 (c) 400 (d) 28
  22. 22.What is the distance between the points (8, 8) and (20, 13)? (a) 13 (b) 14 (c) 169 (d) 17
  23. 23.What is the distance between the points (4, 3) and (8, 6)? (a) 5 (b) 7 (c) 6 (d) 25
  24. 24.What is the midpoint of the line joining (6, 14) and (8, 2)? (a) (7, 8) (b) (8, 7) (c) (14, 16) (d) (1, 6)
  25. 25.In which quadrant does the point (9, 3) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  26. 26.How far is the point (8, 6) from the origin (0, 0)? (a) 11 (b) 10 (c) 14 (d) 100
  27. 27.What is the distance between the points (2, 12) and (26, 5)? (a) 25 (b) 26 (c) 31 (d) 625
  28. 28.What is the distance between the points (2, 11) and (6, 8)? (a) 7 (b) 6 (c) 5 (d) 25
  29. 29.What is the distance between the points (2, 9) and (10, 3)? (a) 14 (b) 11 (c) 10 (d) 100
  30. 30.What is the midpoint of the line joining (6, 13) and (8, 5)? (a) (9, 7) (b) (1, 4) (c) (7, 9) (d) (14, 18)
  31. 31.What is the distance between the points (6, 12) and (14, 6)? (a) 14 (b) 100 (c) 10 (d) 11
  32. 32.How far is the point (8, 15) from the origin (0, 0)? (a) 289 (b) 18 (c) 17 (d) 23
  33. 33.How far is the point (24, 7) from the origin (0, 0)? (a) 25 (b) 625 (c) 26 (d) 31
  34. 34.What is the midpoint of the line joining (6, 0) and (12, 4)? (a) (9, 2) (b) (3, 2) (c) (2, 9) (d) (18, 4)
  35. 35.What is the distance between the points (7, 0) and (13, 8)? (a) 10 (b) 11 (c) 14 (d) 100
  36. 36.How far is the point (12, 5) from the origin (0, 0)? (a) 169 (b) 17 (c) 13 (d) 14
  37. 37.What is the distance between the points (0, 0) and (15, 8)? (a) 18 (b) 17 (c) 289 (d) 23
  38. 38.What is the midpoint of the line joining (5, 7) and (9, 13)? (a) (10, 7) (b) (7, 10) (c) (2, 3) (d) (14, 20)
  39. 39.What is the midpoint of the line joining (10, 12) and (14, 6)? (a) (9, 12) (b) (24, 18) (c) (12, 9) (d) (2, 3)
  40. 40.What is the distance between the points (9, 5) and (14, 17)? (a) 13 (b) 14 (c) 169 (d) 17

Answer key

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

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