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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 545 · 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.How far is the point (8, 15) from the origin (0, 0)? (a) 289 (b) 17 (c) 18 (d) 23
  2. 2.How far is the point (12, 5) from the origin (0, 0)? (a) 17 (b) 13 (c) 14 (d) 169
  3. 3.What is the distance between the points (3, 14) and (8, 2)? (a) 17 (b) 14 (c) 169 (d) 13
  4. 4.What is the midpoint of the line joining (0, 5) and (10, 9)? (a) (7, 5) (b) (10, 14) (c) (5, 2) (d) (5, 7)
  5. 5.In which quadrant does the point (−1, 3) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  6. 6.What is the distance between the points (2, 21) and (14, 5)? (a) 400 (b) 28 (c) 21 (d) 20
  7. 7.What is the distance between the points (3, 2) and (15, 18)? (a) 21 (b) 400 (c) 28 (d) 20
  8. 8.How far is the point (6, 8) from the origin (0, 0)? (a) 11 (b) 10 (c) 100 (d) 14
  9. 9.What is the midpoint of the line joining (6, 4) and (14, 2)? (a) (3, 10) (b) (20, 6) (c) (4, 1) (d) (10, 3)
  10. 10.In which quadrant does the point (−9, −7) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  11. 11.What is the midpoint of the line joining (1, 2) and (3, 14)? (a) (8, 2) (b) (4, 16) (c) (1, 6) (d) (2, 8)
  12. 12.What is the midpoint of the line joining (5, 13) and (11, 5)? (a) (16, 18) (b) (3, 4) (c) (8, 9) (d) (9, 8)
  13. 13.How far is the point (12, 9) from the origin (0, 0)? (a) 225 (b) 16 (c) 21 (d) 15
  14. 14.What is the midpoint of the line joining (0, 11) and (2, 1)? (a) (1, 5) (b) (6, 1) (c) (2, 12) (d) (1, 6)
  15. 15.In which quadrant does the point (−5, −7) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  16. 16.What is the distance between the points (0, 12) and (3, 8)? (a) 7 (b) 5 (c) 25 (d) 6
  17. 17.What is the distance between the points (9, 12) and (21, 3)? (a) 21 (b) 15 (c) 16 (d) 225
  18. 18.In which quadrant does the point (−7, 7) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  19. 19.What is the distance between the points (1, 0) and (25, 7)? (a) 31 (b) 25 (c) 625 (d) 26
  20. 20.What is the midpoint of the line joining (5, 2) and (13, 12)? (a) (18, 14) (b) (9, 7) (c) (4, 5) (d) (7, 9)
  21. 21.In which quadrant does the point (7, 8) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  22. 22.How far is the point (12, 16) from the origin (0, 0)? (a) 400 (b) 28 (c) 20 (d) 21
  23. 23.In which quadrant does the point (1, 9) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  24. 24.What is the distance between the points (8, 7) and (15, 31)? (a) 625 (b) 26 (c) 31 (d) 25
  25. 25.What is the distance between the points (9, 1) and (21, 17)? (a) 28 (b) 21 (c) 20 (d) 400
  26. 26.How far is the point (15, 8) from the origin (0, 0)? (a) 289 (b) 23 (c) 18 (d) 17
  27. 27.What is the distance between the points (7, 5) and (19, 21)? (a) 21 (b) 20 (c) 28 (d) 400
  28. 28.What is the distance between the points (2, 20) and (10, 5)? (a) 17 (b) 289 (c) 23 (d) 18
  29. 29.What is the distance between the points (9, 2) and (13, 5)? (a) 6 (b) 5 (c) 7 (d) 25
  30. 30.What is the distance between the points (0, 0) and (3, 4)? (a) 25 (b) 6 (c) 7 (d) 5
  31. 31.What is the midpoint of the line joining (9, 16) and (19, 8)? (a) (5, 4) (b) (28, 24) (c) (12, 14) (d) (14, 12)
  32. 32.What is the distance between the points (9, 3) and (12, 7)? (a) 6 (b) 25 (c) 5 (d) 7
  33. 33.What is the midpoint of the line joining (7, 4) and (11, 8)? (a) (18, 12) (b) (6, 9) (c) (2, 2) (d) (9, 6)
  34. 34.What is the distance between the points (8, 21) and (17, 9)? (a) 21 (b) 15 (c) 225 (d) 16
  35. 35.In which quadrant does the point (−7, −8) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  36. 36.How far is the point (5, 12) from the origin (0, 0)? (a) 169 (b) 14 (c) 17 (d) 13
  37. 37.What is the distance between the points (5, 2) and (12, 26)? (a) 31 (b) 625 (c) 25 (d) 26
  38. 38.What is the midpoint of the line joining (2, 9) and (12, 19)? (a) (7, 14) (b) (14, 28) (c) (5, 5) (d) (14, 7)
  39. 39.What is the midpoint of the line joining (6, 20) and (8, 8)? (a) (14, 7) (b) (14, 28) (c) (7, 14) (d) (1, 6)
  40. 40.What is the distance between the points (1, 5) and (8, 29)? (a) 31 (b) 26 (c) 25 (d) 625

Answer key

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

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