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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 883 · 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 (2, −4) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  2. 2.What is the midpoint of the line joining (1, 12) and (11, 8)? (a) (10, 6) (b) (6, 10) (c) (5, 2) (d) (12, 20)
  3. 3.What is the distance between the points (9, 9) and (21, 25)? (a) 400 (b) 20 (c) 28 (d) 21
  4. 4.What is the midpoint of the line joining (1, 8) and (9, 20)? (a) (10, 28) (b) (14, 5) (c) (4, 6) (d) (5, 14)
  5. 5.In which quadrant does the point (1, 7) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  6. 6.How far is the point (9, 12) from the origin (0, 0)? (a) 16 (b) 21 (c) 15 (d) 225
  7. 7.What is the midpoint of the line joining (1, 16) and (13, 8)? (a) (12, 7) (b) (7, 12) (c) (14, 24) (d) (6, 4)
  8. 8.What is the distance between the points (5, 3) and (17, 12)? (a) 15 (b) 21 (c) 225 (d) 16
  9. 9.What is the midpoint of the line joining (10, 2) and (22, 14)? (a) (16, 8) (b) (6, 6) (c) (32, 16) (d) (8, 16)
  10. 10.How far is the point (15, 8) from the origin (0, 0)? (a) 18 (b) 23 (c) 17 (d) 289
  11. 11.In which quadrant does the point (−9, 9) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  12. 12.How far is the point (4, 3) from the origin (0, 0)? (a) 6 (b) 5 (c) 25 (d) 7
  13. 13.What is the distance between the points (2, 3) and (11, 15)? (a) 16 (b) 225 (c) 21 (d) 15
  14. 14.What is the distance between the points (3, 30) and (10, 6)? (a) 26 (b) 625 (c) 25 (d) 31
  15. 15.What is the midpoint of the line joining (10, 14) and (14, 8)? (a) (11, 12) (b) (2, 3) (c) (12, 11) (d) (24, 22)
  16. 16.How far is the point (8, 15) from the origin (0, 0)? (a) 289 (b) 23 (c) 18 (d) 17
  17. 17.What is the midpoint of the line joining (7, 16) and (19, 6)? (a) (26, 22) (b) (6, 5) (c) (11, 13) (d) (13, 11)
  18. 18.What is the midpoint of the line joining (10, 3) and (14, 15)? (a) (9, 12) (b) (2, 6) (c) (12, 9) (d) (24, 18)
  19. 19.In which quadrant does the point (−2, −6) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  20. 20.What is the distance between the points (0, 0) and (12, 5)? (a) 13 (b) 17 (c) 14 (d) 169
  21. 21.What is the distance between the points (9, 3) and (18, 15)? (a) 16 (b) 225 (c) 15 (d) 21
  22. 22.What is the distance between the points (9, 9) and (25, 21)? (a) 21 (b) 400 (c) 20 (d) 28
  23. 23.In which quadrant does the point (−1, 5) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  24. 24.In which quadrant does the point (8, 7) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  25. 25.What is the midpoint of the line joining (3, 22) and (15, 10)? (a) (6, 6) (b) (9, 16) (c) (18, 32) (d) (16, 9)
  26. 26.What is the midpoint of the line joining (2, 11) and (14, 9)? (a) (6, 1) (b) (16, 20) (c) (10, 8) (d) (8, 10)
  27. 27.What is the distance between the points (7, 8) and (15, 2)? (a) 100 (b) 14 (c) 10 (d) 11
  28. 28.How far is the point (8, 6) from the origin (0, 0)? (a) 14 (b) 11 (c) 10 (d) 100
  29. 29.What is the distance between the points (8, 5) and (11, 1)? (a) 7 (b) 6 (c) 25 (d) 5
  30. 30.What is the distance between the points (9, 2) and (17, 8)? (a) 10 (b) 14 (c) 11 (d) 100
  31. 31.What is the midpoint of the line joining (5, 20) and (11, 10)? (a) (16, 30) (b) (3, 5) (c) (15, 8) (d) (8, 15)
  32. 32.What is the distance between the points (5, 0) and (20, 8)? (a) 289 (b) 23 (c) 18 (d) 17
  33. 33.How far is the point (12, 16) from the origin (0, 0)? (a) 28 (b) 21 (c) 20 (d) 400
  34. 34.What is the distance between the points (0, 30) and (7, 6)? (a) 31 (b) 625 (c) 26 (d) 25
  35. 35.How far is the point (16, 12) from the origin (0, 0)? (a) 28 (b) 20 (c) 21 (d) 400
  36. 36.How far is the point (7, 24) from the origin (0, 0)? (a) 25 (b) 31 (c) 625 (d) 26
  37. 37.What is the midpoint of the line joining (8, 12) and (10, 2)? (a) (1, 5) (b) (7, 9) (c) (9, 7) (d) (18, 14)
  38. 38.What is the midpoint of the line joining (7, 3) and (15, 15)? (a) (4, 6) (b) (9, 11) (c) (22, 18) (d) (11, 9)
  39. 39.What is the distance between the points (6, 2) and (12, 10)? (a) 100 (b) 10 (c) 14 (d) 11
  40. 40.In which quadrant does the point (6, 8) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant

Answer key

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

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