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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 653 · 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 (5, −6) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  2. 2.What is the midpoint of the line joining (1, 14) and (7, 8)? (a) (3, 3) (b) (8, 22) (c) (11, 4) (d) (4, 11)
  3. 3.In which quadrant does the point (−6, 5) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  4. 4.What is the midpoint of the line joining (6, 0) and (18, 4)? (a) (6, 2) (b) (12, 2) (c) (24, 4) (d) (2, 12)
  5. 5.What is the distance between the points (2, 1) and (9, 25)? (a) 25 (b) 625 (c) 31 (d) 26
  6. 6.What is the midpoint of the line joining (10, 0) and (18, 10)? (a) (28, 10) (b) (14, 5) (c) (4, 5) (d) (5, 14)
  7. 7.What is the distance between the points (6, 7) and (18, 2)? (a) 17 (b) 169 (c) 13 (d) 14
  8. 8.In which quadrant does the point (9, 4) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  9. 9.What is the distance between the points (1, 21) and (10, 9)? (a) 21 (b) 16 (c) 15 (d) 225
  10. 10.In which quadrant does the point (1, 2) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  11. 11.What is the midpoint of the line joining (4, 7) and (14, 13)? (a) (18, 20) (b) (10, 9) (c) (9, 10) (d) (5, 3)
  12. 12.What is the distance between the points (0, 1) and (16, 13)? (a) 28 (b) 20 (c) 400 (d) 21
  13. 13.What is the midpoint of the line joining (3, 18) and (5, 10)? (a) (4, 14) (b) (1, 4) (c) (8, 28) (d) (14, 4)
  14. 14.What is the midpoint of the line joining (2, 2) and (14, 0)? (a) (16, 2) (b) (1, 8) (c) (6, 1) (d) (8, 1)
  15. 15.What is the midpoint of the line joining (7, 11) and (11, 7)? (a) (2, 2) (b) (18, 18) (c) (10, 9) (d) (9, 9)
  16. 16.In which quadrant does the point (−6, −9) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  17. 17.How far is the point (15, 8) from the origin (0, 0)? (a) 17 (b) 289 (c) 23 (d) 18
  18. 18.How far is the point (5, 12) from the origin (0, 0)? (a) 17 (b) 13 (c) 169 (d) 14
  19. 19.In which quadrant does the point (9, 7) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  20. 20.In which quadrant does the point (6, −8) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  21. 21.What is the distance between the points (0, 9) and (16, 21)? (a) 400 (b) 28 (c) 21 (d) 20
  22. 22.What is the distance between the points (1, 15) and (13, 6)? (a) 21 (b) 225 (c) 15 (d) 16
  23. 23.In which quadrant does the point (−3, 7) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  24. 24.What is the distance between the points (0, 8) and (15, 0)? (a) 23 (b) 18 (c) 289 (d) 17
  25. 25.What is the distance between the points (8, 6) and (20, 22)? (a) 20 (b) 28 (c) 400 (d) 21
  26. 26.What is the distance between the points (5, 4) and (11, 12)? (a) 10 (b) 100 (c) 11 (d) 14
  27. 27.In which quadrant does the point (−9, 3) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  28. 28.What is the distance between the points (4, 12) and (16, 3)? (a) 21 (b) 15 (c) 16 (d) 225
  29. 29.What is the midpoint of the line joining (0, 5) and (4, 15)? (a) (4, 20) (b) (10, 2) (c) (2, 5) (d) (2, 10)
  30. 30.What is the midpoint of the line joining (9, 8) and (21, 4)? (a) (30, 12) (b) (6, 15) (c) (6, 2) (d) (15, 6)
  31. 31.What is the distance between the points (2, 7) and (26, 14)? (a) 25 (b) 31 (c) 26 (d) 625
  32. 32.What is the distance between the points (4, 26) and (11, 2)? (a) 26 (b) 31 (c) 625 (d) 25
  33. 33.In which quadrant does the point (−7, 6) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  34. 34.In which quadrant does the point (2, −5) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  35. 35.How far is the point (12, 16) from the origin (0, 0)? (a) 20 (b) 400 (c) 28 (d) 21
  36. 36.What is the midpoint of the line joining (6, 9) and (8, 11)? (a) (14, 20) (b) (10, 7) (c) (1, 1) (d) (7, 10)
  37. 37.In which quadrant does the point (2, −7) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  38. 38.What is the midpoint of the line joining (9, 14) and (11, 2)? (a) (8, 10) (b) (10, 8) (c) (1, 6) (d) (20, 16)
  39. 39.What is the midpoint of the line joining (7, 2) and (11, 6)? (a) (2, 2) (b) (9, 4) (c) (18, 8) (d) (4, 9)
  40. 40.What is the distance between the points (6, 13) and (22, 1)? (a) 28 (b) 400 (c) 21 (d) 20

Answer key

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

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