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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 131 · 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 (0, 12) and (9, 0)? (a) 15 (b) 16 (c) 21 (d) 225
  2. 2.What is the distance between the points (1, 33) and (8, 9)? (a) 625 (b) 31 (c) 26 (d) 25
  3. 3.How far is the point (16, 12) from the origin (0, 0)? (a) 21 (b) 20 (c) 28 (d) 400
  4. 4.What is the distance between the points (0, 9) and (24, 2)? (a) 25 (b) 625 (c) 31 (d) 26
  5. 5.In which quadrant does the point (8, −6) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  6. 6.What is the midpoint of the line joining (4, 1) and (8, 5)? (a) (2, 2) (b) (12, 6) (c) (3, 6) (d) (6, 3)
  7. 7.What is the distance between the points (0, 24) and (8, 9)? (a) 289 (b) 23 (c) 17 (d) 18
  8. 8.What is the midpoint of the line joining (2, 11) and (6, 7)? (a) (2, 2) (b) (4, 9) (c) (8, 18) (d) (9, 4)
  9. 9.In which quadrant does the point (−6, 7) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  10. 10.What is the midpoint of the line joining (6, 5) and (12, 1)? (a) (9, 3) (b) (3, 2) (c) (3, 9) (d) (18, 6)
  11. 11.How far is the point (8, 6) from the origin (0, 0)? (a) 100 (b) 10 (c) 11 (d) 14
  12. 12.In which quadrant does the point (6, −2) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  13. 13.What is the distance between the points (4, 4) and (12, 10)? (a) 10 (b) 14 (c) 11 (d) 100
  14. 14.What is the midpoint of the line joining (0, 9) and (12, 11)? (a) (6, 1) (b) (10, 6) (c) (6, 10) (d) (12, 20)
  15. 15.How far is the point (4, 3) from the origin (0, 0)? (a) 5 (b) 7 (c) 25 (d) 6
  16. 16.What is the distance between the points (0, 15) and (16, 3)? (a) 400 (b) 21 (c) 28 (d) 20
  17. 17.What is the midpoint of the line joining (6, 4) and (8, 10)? (a) (14, 14) (b) (1, 3) (c) (8, 7) (d) (7, 7)
  18. 18.What is the midpoint of the line joining (6, 2) and (12, 8)? (a) (9, 5) (b) (5, 9) (c) (3, 3) (d) (18, 10)
  19. 19.How far is the point (12, 16) from the origin (0, 0)? (a) 20 (b) 21 (c) 28 (d) 400
  20. 20.What is the midpoint of the line joining (7, 10) and (17, 16)? (a) (24, 26) (b) (12, 13) (c) (13, 12) (d) (5, 3)
  21. 21.What is the midpoint of the line joining (10, 8) and (18, 4)? (a) (4, 2) (b) (14, 6) (c) (28, 12) (d) (6, 14)
  22. 22.What is the distance between the points (5, 2) and (9, 5)? (a) 25 (b) 6 (c) 7 (d) 5
  23. 23.In which quadrant does the point (−2, −7) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  24. 24.What is the midpoint of the line joining (1, 5) and (7, 17)? (a) (3, 6) (b) (4, 11) (c) (11, 4) (d) (8, 22)
  25. 25.In which quadrant does the point (1, 4) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  26. 26.What is the distance between the points (7, 3) and (10, 7)? (a) 7 (b) 5 (c) 25 (d) 6
  27. 27.How far is the point (12, 9) from the origin (0, 0)? (a) 225 (b) 16 (c) 15 (d) 21
  28. 28.What is the midpoint of the line joining (10, 9) and (12, 19)? (a) (11, 14) (b) (22, 28) (c) (14, 11) (d) (1, 5)
  29. 29.In which quadrant does the point (−5, −3) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  30. 30.What is the midpoint of the line joining (2, 1) and (6, 9)? (a) (5, 4) (b) (4, 5) (c) (2, 4) (d) (8, 10)
  31. 31.How far is the point (15, 8) from the origin (0, 0)? (a) 17 (b) 23 (c) 289 (d) 18
  32. 32.How far is the point (6, 8) from the origin (0, 0)? (a) 100 (b) 11 (c) 10 (d) 14
  33. 33.In which quadrant does the point (3, −8) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  34. 34.What is the distance between the points (2, 1) and (7, 13)? (a) 169 (b) 13 (c) 14 (d) 17
  35. 35.What is the midpoint of the line joining (9, 0) and (19, 6)? (a) (14, 3) (b) (3, 14) (c) (28, 6) (d) (5, 3)
  36. 36.In which quadrant does the point (8, 8) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  37. 37.What is the distance between the points (7, 9) and (19, 25)? (a) 20 (b) 21 (c) 400 (d) 28
  38. 38.How far is the point (9, 12) from the origin (0, 0)? (a) 15 (b) 225 (c) 21 (d) 16
  39. 39.What is the distance between the points (2, 8) and (9, 32)? (a) 31 (b) 625 (c) 25 (d) 26
  40. 40.What is the midpoint of the line joining (7, 2) and (17, 6)? (a) (5, 2) (b) (24, 8) (c) (4, 12) (d) (12, 4)

Answer key

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

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