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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 820 · 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.In which quadrant does the point (−8, −1) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  2. 2.In which quadrant does the point (−2, −7) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  3. 3.What is the distance between the points (1, 12) and (7, 4)? (a) 11 (b) 100 (c) 10 (d) 14
  4. 4.What is the distance between the points (2, 2) and (14, 18)? (a) 28 (b) 20 (c) 400 (d) 21
  5. 5.In which quadrant does the point (−9, −1) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  6. 6.What is the midpoint of the line joining (3, 22) and (9, 10)? (a) (6, 16) (b) (12, 32) (c) (16, 6) (d) (3, 6)
  7. 7.What is the distance between the points (8, 4) and (15, 28)? (a) 31 (b) 26 (c) 625 (d) 25
  8. 8.In which quadrant does the point (5, −5) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  9. 9.What is the distance between the points (5, 12) and (8, 8)? (a) 6 (b) 5 (c) 25 (d) 7
  10. 10.How far is the point (7, 24) from the origin (0, 0)? (a) 625 (b) 25 (c) 26 (d) 31
  11. 11.How far is the point (5, 12) from the origin (0, 0)? (a) 17 (b) 14 (c) 169 (d) 13
  12. 12.How far is the point (3, 4) from the origin (0, 0)? (a) 6 (b) 25 (c) 5 (d) 7
  13. 13.In which quadrant does the point (−3, 5) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  14. 14.What is the distance between the points (3, 0) and (9, 8)? (a) 14 (b) 100 (c) 10 (d) 11
  15. 15.In which quadrant does the point (4, −6) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  16. 16.What is the midpoint of the line joining (0, 1) and (2, 7)? (a) (1, 4) (b) (4, 1) (c) (2, 8) (d) (1, 3)
  17. 17.What is the midpoint of the line joining (6, 3) and (8, 9)? (a) (14, 12) (b) (6, 7) (c) (1, 3) (d) (7, 6)
  18. 18.What is the midpoint of the line joining (5, 12) and (15, 0)? (a) (6, 10) (b) (20, 12) (c) (5, 6) (d) (10, 6)
  19. 19.How far is the point (4, 3) from the origin (0, 0)? (a) 25 (b) 7 (c) 5 (d) 6
  20. 20.What is the distance between the points (3, 18) and (15, 2)? (a) 21 (b) 28 (c) 20 (d) 400
  21. 21.How far is the point (8, 15) from the origin (0, 0)? (a) 289 (b) 17 (c) 23 (d) 18
  22. 22.What is the midpoint of the line joining (6, 8) and (8, 2)? (a) (1, 3) (b) (14, 10) (c) (5, 7) (d) (7, 5)
  23. 23.What is the midpoint of the line joining (0, 18) and (12, 6)? (a) (12, 6) (b) (6, 12) (c) (12, 24) (d) (6, 6)
  24. 24.What is the midpoint of the line joining (6, 3) and (12, 11)? (a) (3, 4) (b) (18, 14) (c) (7, 9) (d) (9, 7)
  25. 25.What is the midpoint of the line joining (0, 11) and (10, 1)? (a) (10, 12) (b) (5, 5) (c) (6, 5) (d) (5, 6)
  26. 26.What is the distance between the points (0, 9) and (12, 25)? (a) 21 (b) 28 (c) 400 (d) 20
  27. 27.How far is the point (6, 8) from the origin (0, 0)? (a) 11 (b) 10 (c) 14 (d) 100
  28. 28.What is the midpoint of the line joining (5, 3) and (15, 13)? (a) (5, 5) (b) (20, 16) (c) (8, 10) (d) (10, 8)
  29. 29.In which quadrant does the point (−9, 3) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  30. 30.What is the midpoint of the line joining (1, 15) and (5, 7)? (a) (2, 4) (b) (11, 3) (c) (3, 11) (d) (6, 22)
  31. 31.In which quadrant does the point (2, 2) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  32. 32.How far is the point (12, 5) from the origin (0, 0)? (a) 169 (b) 13 (c) 14 (d) 17
  33. 33.What is the distance between the points (0, 6) and (8, 21)? (a) 17 (b) 23 (c) 289 (d) 18
  34. 34.In which quadrant does the point (7, 3) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  35. 35.How far is the point (9, 12) from the origin (0, 0)? (a) 21 (b) 225 (c) 15 (d) 16
  36. 36.What is the midpoint of the line joining (9, 2) and (19, 12)? (a) (5, 5) (b) (7, 14) (c) (28, 14) (d) (14, 7)
  37. 37.In which quadrant does the point (6, 1) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  38. 38.What is the distance between the points (8, 4) and (24, 16)? (a) 400 (b) 28 (c) 20 (d) 21
  39. 39.What is the distance between the points (9, 5) and (21, 14)? (a) 16 (b) 15 (c) 21 (d) 225
  40. 40.What is the midpoint of the line joining (4, 8) and (6, 6)? (a) (10, 14) (b) (5, 7) (c) (7, 5) (d) (1, 1)

Answer key

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

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