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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 620 · 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 midpoint of the line joining (4, 3) and (14, 15)? (a) (18, 18) (b) (5, 6) (c) (10, 9) (d) (9, 9)
  2. 2.In which quadrant does the point (1, 3) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  3. 3.In which quadrant does the point (−1, −3) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  4. 4.How far is the point (5, 12) from the origin (0, 0)? (a) 17 (b) 169 (c) 13 (d) 14
  5. 5.What is the distance between the points (1, 2) and (13, 18)? (a) 20 (b) 400 (c) 21 (d) 28
  6. 6.In which quadrant does the point (8, 2) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  7. 7.How far is the point (12, 16) from the origin (0, 0)? (a) 400 (b) 21 (c) 28 (d) 20
  8. 8.In which quadrant does the point (−2, −6) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  9. 9.What is the midpoint of the line joining (10, 8) and (20, 2)? (a) (30, 10) (b) (5, 15) (c) (5, 3) (d) (15, 5)
  10. 10.In which quadrant does the point (−2, −1) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  11. 11.What is the distance between the points (7, 7) and (12, 19)? (a) 14 (b) 13 (c) 169 (d) 17
  12. 12.What is the distance between the points (2, 17) and (10, 2)? (a) 18 (b) 23 (c) 289 (d) 17
  13. 13.How far is the point (12, 9) from the origin (0, 0)? (a) 225 (b) 21 (c) 16 (d) 15
  14. 14.In which quadrant does the point (−2, −2) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  15. 15.What is the distance between the points (9, 1) and (24, 9)? (a) 23 (b) 17 (c) 289 (d) 18
  16. 16.What is the midpoint of the line joining (3, 15) and (7, 5)? (a) (2, 5) (b) (10, 20) (c) (5, 10) (d) (10, 5)
  17. 17.What is the midpoint of the line joining (8, 3) and (10, 15)? (a) (18, 18) (b) (1, 6) (c) (9, 9) (d) (10, 9)
  18. 18.What is the midpoint of the line joining (1, 1) and (3, 3)? (a) (1, 1) (b) (4, 4) (c) (2, 2) (d) (3, 2)
  19. 19.What is the distance between the points (0, 24) and (12, 8)? (a) 400 (b) 28 (c) 21 (d) 20
  20. 20.In which quadrant does the point (−6, 5) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  21. 21.In which quadrant does the point (2, −3) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  22. 22.In which quadrant does the point (7, 1) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  23. 23.What is the distance between the points (9, 22) and (21, 6)? (a) 20 (b) 28 (c) 400 (d) 21
  24. 24.What is the distance between the points (6, 8) and (18, 17)? (a) 21 (b) 225 (c) 16 (d) 15
  25. 25.What is the midpoint of the line joining (9, 0) and (11, 2)? (a) (10, 1) (b) (1, 1) (c) (1, 10) (d) (20, 2)
  26. 26.What is the distance between the points (7, 13) and (31, 6)? (a) 31 (b) 625 (c) 25 (d) 26
  27. 27.How far is the point (7, 24) from the origin (0, 0)? (a) 31 (b) 25 (c) 26 (d) 625
  28. 28.What is the midpoint of the line joining (0, 15) and (8, 5)? (a) (8, 20) (b) (4, 10) (c) (10, 4) (d) (4, 5)
  29. 29.What is the midpoint of the line joining (8, 0) and (12, 10)? (a) (5, 10) (b) (10, 5) (c) (20, 10) (d) (2, 5)
  30. 30.What is the distance between the points (2, 7) and (8, 15)? (a) 14 (b) 11 (c) 10 (d) 100
  31. 31.In which quadrant does the point (−4, 7) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  32. 32.How far is the point (16, 12) from the origin (0, 0)? (a) 28 (b) 20 (c) 21 (d) 400
  33. 33.How far is the point (3, 4) from the origin (0, 0)? (a) 5 (b) 25 (c) 7 (d) 6
  34. 34.In which quadrant does the point (−5, −5) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  35. 35.What is the midpoint of the line joining (7, 2) and (9, 10)? (a) (1, 4) (b) (6, 8) (c) (8, 6) (d) (16, 12)
  36. 36.What is the midpoint of the line joining (2, 4) and (6, 12)? (a) (4, 8) (b) (8, 4) (c) (8, 16) (d) (2, 4)
  37. 37.In which quadrant does the point (5, 8) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  38. 38.What is the distance between the points (5, 9) and (13, 24)? (a) 18 (b) 23 (c) 289 (d) 17
  39. 39.In which quadrant does the point (1, −2) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  40. 40.How far is the point (6, 8) from the origin (0, 0)? (a) 11 (b) 14 (c) 100 (d) 10

Answer key

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

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