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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 682 · 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 (4, 7) and (12, 1)? (a) 100 (b) 14 (c) 11 (d) 10
  2. 2.What is the distance between the points (2, 28) and (9, 4)? (a) 25 (b) 26 (c) 31 (d) 625
  3. 3.In which quadrant does the point (−6, 1) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  4. 4.How far is the point (6, 8) from the origin (0, 0)? (a) 11 (b) 100 (c) 10 (d) 14
  5. 5.How far is the point (8, 6) from the origin (0, 0)? (a) 14 (b) 10 (c) 11 (d) 100
  6. 6.What is the distance between the points (5, 16) and (10, 4)? (a) 14 (b) 17 (c) 13 (d) 169
  7. 7.In which quadrant does the point (1, 6) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  8. 8.What is the distance between the points (7, 22) and (19, 6)? (a) 400 (b) 20 (c) 28 (d) 21
  9. 9.How far is the point (15, 8) from the origin (0, 0)? (a) 289 (b) 23 (c) 18 (d) 17
  10. 10.What is the midpoint of the line joining (2, 12) and (8, 2)? (a) (3, 5) (b) (10, 14) (c) (7, 5) (d) (5, 7)
  11. 11.In which quadrant does the point (−2, 4) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  12. 12.What is the distance between the points (5, 15) and (10, 3)? (a) 169 (b) 17 (c) 13 (d) 14
  13. 13.In which quadrant does the point (4, 3) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  14. 14.How far is the point (12, 5) from the origin (0, 0)? (a) 17 (b) 14 (c) 13 (d) 169
  15. 15.What is the midpoint of the line joining (8, 12) and (12, 8)? (a) (2, 2) (b) (10, 10) (c) (20, 20) (d) (11, 10)
  16. 16.What is the distance between the points (1, 11) and (13, 2)? (a) 15 (b) 225 (c) 21 (d) 16
  17. 17.What is the distance between the points (3, 10) and (15, 1)? (a) 16 (b) 21 (c) 15 (d) 225
  18. 18.How far is the point (4, 3) from the origin (0, 0)? (a) 6 (b) 7 (c) 5 (d) 25
  19. 19.In which quadrant does the point (−9, 5) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  20. 20.What is the midpoint of the line joining (10, 10) and (22, 2)? (a) (32, 12) (b) (6, 16) (c) (6, 4) (d) (16, 6)
  21. 21.How far is the point (12, 16) from the origin (0, 0)? (a) 20 (b) 400 (c) 28 (d) 21
  22. 22.What is the midpoint of the line joining (2, 10) and (10, 20)? (a) (6, 15) (b) (12, 30) (c) (15, 6) (d) (4, 5)
  23. 23.How far is the point (5, 12) from the origin (0, 0)? (a) 14 (b) 13 (c) 17 (d) 169
  24. 24.What is the midpoint of the line joining (2, 2) and (8, 4)? (a) (10, 6) (b) (5, 3) (c) (3, 5) (d) (3, 1)
  25. 25.What is the midpoint of the line joining (1, 3) and (5, 7)? (a) (5, 3) (b) (3, 5) (c) (6, 10) (d) (2, 2)
  26. 26.How far is the point (9, 12) from the origin (0, 0)? (a) 16 (b) 225 (c) 15 (d) 21
  27. 27.What is the midpoint of the line joining (5, 3) and (15, 1)? (a) (2, 10) (b) (5, 1) (c) (20, 4) (d) (10, 2)
  28. 28.What is the distance between the points (7, 0) and (12, 12)? (a) 169 (b) 14 (c) 17 (d) 13
  29. 29.How far is the point (3, 4) from the origin (0, 0)? (a) 7 (b) 6 (c) 25 (d) 5
  30. 30.What is the midpoint of the line joining (1, 6) and (5, 16)? (a) (11, 3) (b) (2, 5) (c) (6, 22) (d) (3, 11)
  31. 31.In which quadrant does the point (−1, 2) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  32. 32.What is the midpoint of the line joining (3, 9) and (15, 11)? (a) (18, 20) (b) (6, 1) (c) (10, 9) (d) (9, 10)
  33. 33.What is the midpoint of the line joining (1, 1) and (3, 5)? (a) (4, 6) (b) (1, 2) (c) (3, 2) (d) (2, 3)
  34. 34.What is the midpoint of the line joining (6, 9) and (8, 11)? (a) (14, 20) (b) (1, 1) (c) (7, 10) (d) (10, 7)
  35. 35.In which quadrant does the point (2, −6) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  36. 36.In which quadrant does the point (8, −8) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  37. 37.What is the distance between the points (5, 1) and (12, 25)? (a) 625 (b) 25 (c) 26 (d) 31
  38. 38.What is the distance between the points (0, 19) and (16, 7)? (a) 21 (b) 20 (c) 28 (d) 400
  39. 39.What is the midpoint of the line joining (0, 8) and (2, 10)? (a) (1, 1) (b) (2, 18) (c) (9, 1) (d) (1, 9)
  40. 40.What is the distance between the points (9, 3) and (18, 15)? (a) 16 (b) 15 (c) 21 (d) 225

Answer key

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

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