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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 667 · 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 (9, 8) and (16, 32)? (a) 31 (b) 625 (c) 25 (d) 26
  2. 2.How far is the point (7, 24) from the origin (0, 0)? (a) 26 (b) 625 (c) 25 (d) 31
  3. 3.In which quadrant does the point (8, 2) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  4. 4.In which quadrant does the point (−4, −1) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  5. 5.In which quadrant does the point (2, −6) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
  6. 6.What is the distance between the points (0, 9) and (12, 25)? (a) 20 (b) 400 (c) 21 (d) 28
  7. 7.What is the distance between the points (4, 2) and (28, 9)? (a) 26 (b) 25 (c) 31 (d) 625
  8. 8.What is the midpoint of the line joining (9, 9) and (21, 17)? (a) (15, 13) (b) (30, 26) (c) (6, 4) (d) (13, 15)
  9. 9.What is the distance between the points (6, 4) and (9, 8)? (a) 6 (b) 25 (c) 5 (d) 7
  10. 10.In which quadrant does the point (9, 3) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  11. 11.What is the distance between the points (8, 5) and (14, 13)? (a) 100 (b) 11 (c) 14 (d) 10
  12. 12.What is the midpoint of the line joining (6, 7) and (14, 11)? (a) (4, 2) (b) (10, 9) (c) (9, 10) (d) (20, 18)
  13. 13.What is the midpoint of the line joining (8, 8) and (10, 14)? (a) (1, 3) (b) (18, 22) (c) (11, 9) (d) (9, 11)
  14. 14.What is the distance between the points (3, 1) and (18, 9)? (a) 18 (b) 23 (c) 17 (d) 289
  15. 15.What is the midpoint of the line joining (8, 11) and (16, 3)? (a) (24, 14) (b) (12, 7) (c) (4, 4) (d) (7, 12)
  16. 16.How far is the point (8, 15) from the origin (0, 0)? (a) 23 (b) 18 (c) 289 (d) 17
  17. 17.In which quadrant does the point (−8, −6) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  18. 18.What is the midpoint of the line joining (3, 0) and (7, 2)? (a) (10, 2) (b) (5, 1) (c) (2, 1) (d) (1, 5)
  19. 19.How far is the point (24, 7) from the origin (0, 0)? (a) 31 (b) 25 (c) 26 (d) 625
  20. 20.What is the midpoint of the line joining (9, 9) and (15, 15)? (a) (24, 24) (b) (3, 3) (c) (13, 12) (d) (12, 12)
  21. 21.What is the distance between the points (2, 5) and (6, 2)? (a) 6 (b) 5 (c) 7 (d) 25
  22. 22.What is the distance between the points (0, 20) and (12, 4)? (a) 20 (b) 400 (c) 21 (d) 28
  23. 23.How far is the point (15, 8) from the origin (0, 0)? (a) 17 (b) 289 (c) 23 (d) 18
  24. 24.What is the distance between the points (2, 1) and (5, 5)? (a) 25 (b) 5 (c) 6 (d) 7
  25. 25.What is the midpoint of the line joining (0, 10) and (6, 16)? (a) (6, 26) (b) (3, 13) (c) (3, 3) (d) (13, 3)
  26. 26.What is the midpoint of the line joining (10, 11) and (16, 5)? (a) (26, 16) (b) (3, 3) (c) (13, 8) (d) (8, 13)
  27. 27.What is the distance between the points (1, 21) and (13, 5)? (a) 21 (b) 400 (c) 20 (d) 28
  28. 28.In which quadrant does the point (7, 1) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  29. 29.In which quadrant does the point (3, 3) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  30. 30.In which quadrant does the point (−3, −2) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  31. 31.What is the distance between the points (2, 16) and (18, 4)? (a) 21 (b) 20 (c) 28 (d) 400
  32. 32.How far is the point (3, 4) from the origin (0, 0)? (a) 25 (b) 7 (c) 6 (d) 5
  33. 33.What is the midpoint of the line joining (10, 4) and (14, 0)? (a) (12, 2) (b) (24, 4) (c) (2, 2) (d) (2, 12)
  34. 34.In which quadrant does the point (8, 4) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  35. 35.How far is the point (12, 16) from the origin (0, 0)? (a) 28 (b) 21 (c) 20 (d) 400
  36. 36.What is the distance between the points (0, 0) and (12, 5)? (a) 17 (b) 169 (c) 13 (d) 14
  37. 37.In which quadrant does the point (7, 3) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  38. 38.How far is the point (6, 8) from the origin (0, 0)? (a) 14 (b) 100 (c) 10 (d) 11
  39. 39.What is the distance between the points (6, 6) and (14, 21)? (a) 289 (b) 17 (c) 23 (d) 18
  40. 40.What is the distance between the points (8, 8) and (20, 17)? (a) 16 (b) 15 (c) 21 (d) 225

Answer key

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

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