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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 836 · 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 (7, −1) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  2. 2.How far is the point (15, 8) from the origin (0, 0)? (a) 289 (b) 18 (c) 23 (d) 17
  3. 3.What is the distance between the points (8, 1) and (15, 25)? (a) 31 (b) 625 (c) 26 (d) 25
  4. 4.What is the distance between the points (9, 7) and (13, 10)? (a) 25 (b) 5 (c) 7 (d) 6
  5. 5.What is the distance between the points (7, 8) and (22, 16)? (a) 23 (b) 289 (c) 18 (d) 17
  6. 6.In which quadrant does the point (8, 6) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  7. 7.What is the midpoint of the line joining (5, 2) and (9, 10)? (a) (7, 6) (b) (14, 12) (c) (2, 4) (d) (6, 7)
  8. 8.What is the midpoint of the line joining (0, 6) and (8, 2)? (a) (5, 4) (b) (4, 2) (c) (8, 8) (d) (4, 4)
  9. 9.What is the midpoint of the line joining (3, 10) and (13, 22)? (a) (16, 8) (b) (5, 6) (c) (8, 16) (d) (16, 32)
  10. 10.How far is the point (3, 4) from the origin (0, 0)? (a) 25 (b) 7 (c) 6 (d) 5
  11. 11.What is the distance between the points (1, 13) and (7, 5)? (a) 11 (b) 10 (c) 100 (d) 14
  12. 12.What is the midpoint of the line joining (4, 2) and (14, 8)? (a) (5, 9) (b) (9, 5) (c) (18, 10) (d) (5, 3)
  13. 13.What is the distance between the points (6, 0) and (22, 12)? (a) 28 (b) 20 (c) 400 (d) 21
  14. 14.What is the midpoint of the line joining (3, 16) and (7, 8)? (a) (12, 5) (b) (5, 12) (c) (10, 24) (d) (2, 4)
  15. 15.What is the midpoint of the line joining (8, 18) and (18, 8)? (a) (5, 5) (b) (26, 26) (c) (14, 13) (d) (13, 13)
  16. 16.In which quadrant does the point (8, 2) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  17. 17.In which quadrant does the point (−8, 4) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  18. 18.What is the distance between the points (4, 1) and (16, 17)? (a) 400 (b) 21 (c) 28 (d) 20
  19. 19.In which quadrant does the point (2, 1) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  20. 20.What is the midpoint of the line joining (10, 8) and (12, 10)? (a) (1, 1) (b) (11, 9) (c) (22, 18) (d) (9, 11)
  21. 21.What is the distance between the points (1, 13) and (4, 9)? (a) 6 (b) 5 (c) 25 (d) 7
  22. 22.How far is the point (12, 16) from the origin (0, 0)? (a) 28 (b) 20 (c) 21 (d) 400
  23. 23.What is the midpoint of the line joining (5, 8) and (15, 16)? (a) (12, 10) (b) (20, 24) (c) (5, 4) (d) (10, 12)
  24. 24.What is the distance between the points (0, 2) and (8, 8)? (a) 11 (b) 10 (c) 14 (d) 100
  25. 25.What is the distance between the points (0, 3) and (12, 12)? (a) 225 (b) 16 (c) 21 (d) 15
  26. 26.What is the distance between the points (1, 7) and (9, 22)? (a) 289 (b) 17 (c) 23 (d) 18
  27. 27.What is the distance between the points (9, 8) and (33, 15)? (a) 26 (b) 625 (c) 25 (d) 31
  28. 28.In which quadrant does the point (−1, 1) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  29. 29.What is the distance between the points (2, 26) and (9, 2)? (a) 31 (b) 625 (c) 25 (d) 26
  30. 30.In which quadrant does the point (−2, 9) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  31. 31.What is the distance between the points (8, 4) and (11, 0)? (a) 6 (b) 7 (c) 5 (d) 25
  32. 32.How far is the point (8, 6) from the origin (0, 0)? (a) 10 (b) 14 (c) 11 (d) 100
  33. 33.What is the distance between the points (0, 1) and (15, 9)? (a) 289 (b) 17 (c) 18 (d) 23
  34. 34.In which quadrant does the point (−2, 5) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
  35. 35.How far is the point (8, 15) from the origin (0, 0)? (a) 18 (b) 289 (c) 17 (d) 23
  36. 36.In which quadrant does the point (−7, −6) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  37. 37.What is the distance between the points (1, 1) and (9, 7)? (a) 11 (b) 14 (c) 100 (d) 10
  38. 38.What is the distance between the points (5, 20) and (21, 8)? (a) 28 (b) 400 (c) 21 (d) 20
  39. 39.What is the distance between the points (3, 12) and (9, 4)? (a) 11 (b) 14 (c) 10 (d) 100
  40. 40.What is the midpoint of the line joining (2, 0) and (12, 12)? (a) (14, 12) (b) (5, 6) (c) (7, 6) (d) (6, 7)

Answer key

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

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