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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 223 · 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 (5, 0) and (29, 7)? (a) 26 (b) 625 (c) 25 (d) 31
  2. 2.What is the midpoint of the line joining (6, 22) and (16, 10)? (a) (11, 16) (b) (16, 11) (c) (5, 6) (d) (22, 32)
  3. 3.In which quadrant does the point (2, 3) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  4. 4.How far is the point (8, 15) from the origin (0, 0)? (a) 18 (b) 289 (c) 17 (d) 23
  5. 5.What is the distance between the points (6, 31) and (13, 7)? (a) 625 (b) 25 (c) 31 (d) 26
  6. 6.What is the distance between the points (0, 4) and (4, 7)? (a) 5 (b) 7 (c) 6 (d) 25
  7. 7.What is the distance between the points (6, 10) and (9, 6)? (a) 7 (b) 5 (c) 6 (d) 25
  8. 8.How far is the point (24, 7) from the origin (0, 0)? (a) 26 (b) 625 (c) 31 (d) 25
  9. 9.How far is the point (12, 9) from the origin (0, 0)? (a) 16 (b) 225 (c) 21 (d) 15
  10. 10.In which quadrant does the point (−7, 7) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  11. 11.How far is the point (3, 4) from the origin (0, 0)? (a) 25 (b) 6 (c) 5 (d) 7
  12. 12.How far is the point (8, 6) from the origin (0, 0)? (a) 14 (b) 11 (c) 100 (d) 10
  13. 13.What is the distance between the points (3, 14) and (19, 2)? (a) 28 (b) 400 (c) 20 (d) 21
  14. 14.How far is the point (9, 12) from the origin (0, 0)? (a) 21 (b) 15 (c) 16 (d) 225
  15. 15.What is the distance between the points (3, 1) and (8, 13)? (a) 14 (b) 169 (c) 13 (d) 17
  16. 16.What is the midpoint of the line joining (2, 3) and (8, 9)? (a) (6, 5) (b) (3, 3) (c) (10, 12) (d) (5, 6)
  17. 17.What is the distance between the points (1, 5) and (7, 13)? (a) 14 (b) 11 (c) 100 (d) 10
  18. 18.What is the distance between the points (6, 6) and (11, 18)? (a) 13 (b) 169 (c) 14 (d) 17
  19. 19.How far is the point (5, 12) from the origin (0, 0)? (a) 14 (b) 17 (c) 13 (d) 169
  20. 20.What is the distance between the points (7, 4) and (19, 13)? (a) 15 (b) 21 (c) 225 (d) 16
  21. 21.What is the distance between the points (3, 1) and (6, 5)? (a) 6 (b) 25 (c) 7 (d) 5
  22. 22.In which quadrant does the point (−3, 9) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
  23. 23.How far is the point (16, 12) from the origin (0, 0)? (a) 28 (b) 400 (c) 21 (d) 20
  24. 24.How far is the point (12, 5) from the origin (0, 0)? (a) 17 (b) 169 (c) 14 (d) 13
  25. 25.What is the distance between the points (2, 3) and (14, 12)? (a) 16 (b) 15 (c) 225 (d) 21
  26. 26.How far is the point (15, 8) from the origin (0, 0)? (a) 18 (b) 289 (c) 23 (d) 17
  27. 27.What is the midpoint of the line joining (4, 9) and (14, 1)? (a) (5, 9) (b) (9, 5) (c) (18, 10) (d) (5, 4)
  28. 28.What is the distance between the points (2, 16) and (14, 7)? (a) 16 (b) 225 (c) 21 (d) 15
  29. 29.What is the distance between the points (0, 6) and (8, 0)? (a) 11 (b) 14 (c) 10 (d) 100
  30. 30.What is the distance between the points (0, 2) and (16, 14)? (a) 400 (b) 21 (c) 28 (d) 20
  31. 31.What is the midpoint of the line joining (8, 9) and (16, 3)? (a) (24, 12) (b) (12, 6) (c) (6, 12) (d) (4, 3)
  32. 32.What is the distance between the points (2, 2) and (26, 9)? (a) 625 (b) 31 (c) 25 (d) 26
  33. 33.How far is the point (4, 3) from the origin (0, 0)? (a) 6 (b) 25 (c) 5 (d) 7
  34. 34.What is the midpoint of the line joining (8, 1) and (14, 13)? (a) (11, 7) (b) (3, 6) (c) (7, 11) (d) (22, 14)
  35. 35.What is the midpoint of the line joining (4, 5) and (14, 11)? (a) (9, 8) (b) (5, 3) (c) (18, 16) (d) (8, 9)
  36. 36.In which quadrant does the point (3, −7) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  37. 37.In which quadrant does the point (6, 9) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  38. 38.What is the distance between the points (1, 1) and (5, 4)? (a) 25 (b) 6 (c) 5 (d) 7
  39. 39.What is the distance between the points (9, 2) and (17, 8)? (a) 100 (b) 14 (c) 11 (d) 10
  40. 40.What is the distance between the points (2, 8) and (10, 2)? (a) 100 (b) 10 (c) 11 (d) 14

Answer key

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

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