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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 443 · 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, 3) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  2. 2.How far is the point (16, 12) from the origin (0, 0)? (a) 28 (b) 20 (c) 400 (d) 21
  3. 3.How far is the point (12, 9) from the origin (0, 0)? (a) 15 (b) 21 (c) 16 (d) 225
  4. 4.How far is the point (12, 16) from the origin (0, 0)? (a) 400 (b) 28 (c) 20 (d) 21
  5. 5.What is the distance between the points (1, 7) and (7, 15)? (a) 10 (b) 11 (c) 14 (d) 100
  6. 6.What is the midpoint of the line joining (4, 15) and (14, 7)? (a) (18, 22) (b) (5, 4) (c) (9, 11) (d) (11, 9)
  7. 7.What is the midpoint of the line joining (5, 6) and (17, 8)? (a) (22, 14) (b) (11, 7) (c) (7, 11) (d) (6, 1)
  8. 8.In which quadrant does the point (−2, −6) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  9. 9.What is the distance between the points (0, 4) and (16, 16)? (a) 28 (b) 20 (c) 400 (d) 21
  10. 10.What is the distance between the points (1, 7) and (25, 0)? (a) 31 (b) 625 (c) 26 (d) 25
  11. 11.In which quadrant does the point (−1, −8) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  12. 12.What is the midpoint of the line joining (0, 1) and (4, 11)? (a) (6, 2) (b) (2, 5) (c) (4, 12) (d) (2, 6)
  13. 13.What is the distance between the points (1, 8) and (13, 17)? (a) 225 (b) 21 (c) 16 (d) 15
  14. 14.How far is the point (8, 6) from the origin (0, 0)? (a) 14 (b) 11 (c) 100 (d) 10
  15. 15.In which quadrant does the point (−6, −2) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  16. 16.How far is the point (4, 3) from the origin (0, 0)? (a) 7 (b) 25 (c) 6 (d) 5
  17. 17.In which quadrant does the point (3, 5) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  18. 18.What is the distance between the points (2, 4) and (5, 0)? (a) 6 (b) 7 (c) 25 (d) 5
  19. 19.What is the distance between the points (0, 9) and (8, 3)? (a) 11 (b) 10 (c) 14 (d) 100
  20. 20.How far is the point (7, 24) from the origin (0, 0)? (a) 625 (b) 31 (c) 26 (d) 25
  21. 21.How far is the point (12, 5) from the origin (0, 0)? (a) 169 (b) 17 (c) 14 (d) 13
  22. 22.What is the midpoint of the line joining (9, 0) and (15, 4)? (a) (2, 12) (b) (3, 2) (c) (12, 2) (d) (24, 4)
  23. 23.In which quadrant does the point (3, 8) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  24. 24.How far is the point (5, 12) from the origin (0, 0)? (a) 14 (b) 169 (c) 17 (d) 13
  25. 25.What is the distance between the points (2, 2) and (18, 14)? (a) 400 (b) 20 (c) 28 (d) 21
  26. 26.In which quadrant does the point (−6, 9) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  27. 27.How far is the point (3, 4) from the origin (0, 0)? (a) 25 (b) 5 (c) 6 (d) 7
  28. 28.What is the midpoint of the line joining (1, 2) and (5, 8)? (a) (3, 5) (b) (2, 3) (c) (6, 10) (d) (5, 3)
  29. 29.In which quadrant does the point (−2, 8) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  30. 30.What is the distance between the points (2, 2) and (14, 18)? (a) 28 (b) 20 (c) 21 (d) 400
  31. 31.What is the distance between the points (3, 10) and (15, 1)? (a) 21 (b) 225 (c) 16 (d) 15
  32. 32.What is the midpoint of the line joining (3, 16) and (9, 4)? (a) (3, 6) (b) (12, 20) (c) (6, 10) (d) (10, 6)
  33. 33.What is the distance between the points (1, 2) and (13, 7)? (a) 17 (b) 14 (c) 13 (d) 169
  34. 34.What is the midpoint of the line joining (10, 17) and (22, 5)? (a) (16, 11) (b) (32, 22) (c) (6, 6) (d) (11, 16)
  35. 35.What is the distance between the points (0, 0) and (4, 3)? (a) 25 (b) 7 (c) 6 (d) 5
  36. 36.What is the distance between the points (3, 21) and (19, 9)? (a) 28 (b) 21 (c) 400 (d) 20
  37. 37.What is the distance between the points (9, 4) and (15, 12)? (a) 11 (b) 14 (c) 10 (d) 100
  38. 38.What is the midpoint of the line joining (2, 1) and (8, 7)? (a) (10, 8) (b) (4, 5) (c) (5, 4) (d) (3, 3)
  39. 39.What is the midpoint of the line joining (6, 8) and (10, 0)? (a) (16, 8) (b) (4, 8) (c) (2, 4) (d) (8, 4)
  40. 40.What is the midpoint of the line joining (1, 7) and (3, 9)? (a) (4, 16) (b) (8, 2) (c) (2, 8) (d) (1, 1)

Answer key

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

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