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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 726 · 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 (16, 12) from the origin (0, 0)? (a) 20 (b) 400 (c) 21 (d) 28
  2. 2.In which quadrant does the point (8, −6) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
  3. 3.How far is the point (24, 7) from the origin (0, 0)? (a) 25 (b) 31 (c) 625 (d) 26
  4. 4.How far is the point (9, 12) from the origin (0, 0)? (a) 225 (b) 15 (c) 21 (d) 16
  5. 5.How far is the point (7, 24) from the origin (0, 0)? (a) 625 (b) 31 (c) 25 (d) 26
  6. 6.What is the distance between the points (3, 2) and (11, 8)? (a) 10 (b) 11 (c) 14 (d) 100
  7. 7.What is the midpoint of the line joining (5, 2) and (11, 12)? (a) (8, 7) (b) (16, 14) (c) (3, 5) (d) (7, 8)
  8. 8.What is the distance between the points (7, 2) and (11, 5)? (a) 6 (b) 7 (c) 25 (d) 5
  9. 9.What is the midpoint of the line joining (4, 3) and (16, 5)? (a) (10, 4) (b) (6, 1) (c) (4, 10) (d) (20, 8)
  10. 10.How far is the point (8, 15) from the origin (0, 0)? (a) 23 (b) 17 (c) 289 (d) 18
  11. 11.How far is the point (8, 6) from the origin (0, 0)? (a) 11 (b) 14 (c) 10 (d) 100
  12. 12.How far is the point (5, 12) from the origin (0, 0)? (a) 13 (b) 14 (c) 169 (d) 17
  13. 13.How far is the point (12, 16) from the origin (0, 0)? (a) 20 (b) 21 (c) 28 (d) 400
  14. 14.What is the midpoint of the line joining (7, 9) and (11, 19)? (a) (2, 5) (b) (18, 28) (c) (9, 14) (d) (14, 9)
  15. 15.In which quadrant does the point (7, −2) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  16. 16.In which quadrant does the point (−9, 9) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  17. 17.What is the midpoint of the line joining (10, 10) and (14, 14)? (a) (13, 12) (b) (12, 12) (c) (2, 2) (d) (24, 24)
  18. 18.What is the midpoint of the line joining (6, 11) and (18, 7)? (a) (12, 9) (b) (9, 12) (c) (6, 2) (d) (24, 18)
  19. 19.In which quadrant does the point (2, −7) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
  20. 20.What is the distance between the points (6, 0) and (9, 4)? (a) 5 (b) 7 (c) 6 (d) 25
  21. 21.What is the distance between the points (3, 21) and (8, 9)? (a) 13 (b) 14 (c) 169 (d) 17
  22. 22.What is the midpoint of the line joining (4, 10) and (16, 16)? (a) (6, 3) (b) (20, 26) (c) (13, 10) (d) (10, 13)
  23. 23.What is the midpoint of the line joining (2, 5) and (10, 7)? (a) (7, 6) (b) (12, 12) (c) (6, 6) (d) (4, 1)
  24. 24.What is the midpoint of the line joining (6, 13) and (8, 1)? (a) (1, 6) (b) (7, 7) (c) (8, 7) (d) (14, 14)
  25. 25.What is the distance between the points (4, 8) and (9, 20)? (a) 17 (b) 169 (c) 13 (d) 14
  26. 26.What is the midpoint of the line joining (10, 9) and (18, 3)? (a) (4, 3) (b) (6, 14) (c) (28, 12) (d) (14, 6)
  27. 27.What is the distance between the points (2, 8) and (10, 14)? (a) 11 (b) 14 (c) 100 (d) 10
  28. 28.What is the distance between the points (1, 4) and (9, 19)? (a) 289 (b) 17 (c) 18 (d) 23
  29. 29.What is the distance between the points (0, 4) and (3, 0)? (a) 7 (b) 5 (c) 6 (d) 25
  30. 30.What is the midpoint of the line joining (4, 6) and (14, 8)? (a) (9, 7) (b) (5, 1) (c) (7, 9) (d) (18, 14)
  31. 31.What is the midpoint of the line joining (2, 20) and (4, 8)? (a) (6, 28) (b) (1, 6) (c) (3, 14) (d) (14, 3)
  32. 32.What is the distance between the points (2, 6) and (26, 13)? (a) 26 (b) 625 (c) 31 (d) 25
  33. 33.What is the distance between the points (0, 1) and (5, 13)? (a) 14 (b) 17 (c) 13 (d) 169
  34. 34.How far is the point (6, 8) from the origin (0, 0)? (a) 100 (b) 11 (c) 10 (d) 14
  35. 35.In which quadrant does the point (−9, 2) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  36. 36.What is the midpoint of the line joining (5, 0) and (11, 8)? (a) (8, 4) (b) (3, 4) (c) (4, 8) (d) (16, 8)
  37. 37.In which quadrant does the point (4, 7) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  38. 38.What is the distance between the points (0, 4) and (12, 9)? (a) 169 (b) 14 (c) 13 (d) 17
  39. 39.What is the midpoint of the line joining (1, 11) and (5, 3)? (a) (6, 14) (b) (7, 3) (c) (3, 7) (d) (2, 4)
  40. 40.How far is the point (3, 4) from the origin (0, 0)? (a) 6 (b) 7 (c) 5 (d) 25

Answer key

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

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