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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 598 · 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, 4) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  2. 2.In which quadrant does the point (−6, −1) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  3. 3.In which quadrant does the point (1, −1) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  4. 4.What is the midpoint of the line joining (2, 3) and (14, 1)? (a) (6, 1) (b) (2, 8) (c) (16, 4) (d) (8, 2)
  5. 5.What is the midpoint of the line joining (3, 5) and (7, 7)? (a) (2, 1) (b) (6, 5) (c) (10, 12) (d) (5, 6)
  6. 6.How far is the point (3, 4) from the origin (0, 0)? (a) 7 (b) 5 (c) 25 (d) 6
  7. 7.What is the distance between the points (0, 0) and (12, 5)? (a) 14 (b) 169 (c) 17 (d) 13
  8. 8.In which quadrant does the point (3, −2) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  9. 9.What is the midpoint of the line joining (9, 5) and (17, 1)? (a) (26, 6) (b) (3, 13) (c) (13, 3) (d) (4, 2)
  10. 10.What is the midpoint of the line joining (3, 16) and (5, 4)? (a) (1, 6) (b) (10, 4) (c) (8, 20) (d) (4, 10)
  11. 11.How far is the point (6, 8) from the origin (0, 0)? (a) 14 (b) 10 (c) 100 (d) 11
  12. 12.What is the midpoint of the line joining (6, 3) and (8, 15)? (a) (7, 9) (b) (1, 6) (c) (14, 18) (d) (9, 7)
  13. 13.How far is the point (9, 12) from the origin (0, 0)? (a) 21 (b) 225 (c) 16 (d) 15
  14. 14.What is the midpoint of the line joining (8, 11) and (14, 5)? (a) (8, 11) (b) (22, 16) (c) (3, 3) (d) (11, 8)
  15. 15.How far is the point (16, 12) from the origin (0, 0)? (a) 20 (b) 21 (c) 400 (d) 28
  16. 16.What is the midpoint of the line joining (9, 20) and (15, 8)? (a) (3, 6) (b) (12, 14) (c) (14, 12) (d) (24, 28)
  17. 17.How far is the point (12, 16) from the origin (0, 0)? (a) 28 (b) 20 (c) 21 (d) 400
  18. 18.How far is the point (8, 15) from the origin (0, 0)? (a) 17 (b) 289 (c) 18 (d) 23
  19. 19.What is the distance between the points (4, 25) and (11, 1)? (a) 25 (b) 625 (c) 26 (d) 31
  20. 20.What is the distance between the points (6, 18) and (22, 6)? (a) 21 (b) 400 (c) 20 (d) 28
  21. 21.What is the distance between the points (3, 3) and (8, 15)? (a) 169 (b) 17 (c) 13 (d) 14
  22. 22.What is the distance between the points (2, 12) and (14, 3)? (a) 225 (b) 21 (c) 16 (d) 15
  23. 23.What is the distance between the points (4, 5) and (16, 0)? (a) 14 (b) 169 (c) 13 (d) 17
  24. 24.What is the distance between the points (9, 6) and (21, 15)? (a) 15 (b) 16 (c) 21 (d) 225
  25. 25.How far is the point (15, 8) from the origin (0, 0)? (a) 18 (b) 23 (c) 17 (d) 289
  26. 26.What is the midpoint of the line joining (3, 4) and (11, 14)? (a) (4, 5) (b) (7, 9) (c) (14, 18) (d) (9, 7)
  27. 27.What is the distance between the points (1, 14) and (17, 2)? (a) 21 (b) 20 (c) 28 (d) 400
  28. 28.What is the midpoint of the line joining (4, 7) and (8, 3)? (a) (5, 6) (b) (2, 2) (c) (6, 5) (d) (12, 10)
  29. 29.In which quadrant does the point (2, −6) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  30. 30.What is the distance between the points (3, 8) and (7, 5)? (a) 7 (b) 6 (c) 5 (d) 25
  31. 31.What is the midpoint of the line joining (1, 6) and (13, 14)? (a) (6, 4) (b) (10, 7) (c) (14, 20) (d) (7, 10)
  32. 32.What is the midpoint of the line joining (6, 8) and (18, 20)? (a) (6, 6) (b) (12, 14) (c) (14, 12) (d) (24, 28)
  33. 33.In which quadrant does the point (−5, 1) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  34. 34.What is the midpoint of the line joining (6, 13) and (14, 3)? (a) (10, 8) (b) (4, 5) (c) (20, 16) (d) (8, 10)
  35. 35.What is the midpoint of the line joining (5, 9) and (9, 7)? (a) (14, 16) (b) (8, 7) (c) (7, 8) (d) (2, 1)
  36. 36.What is the midpoint of the line joining (2, 0) and (6, 6)? (a) (3, 4) (b) (4, 3) (c) (2, 3) (d) (8, 6)
  37. 37.What is the distance between the points (4, 7) and (13, 19)? (a) 21 (b) 16 (c) 15 (d) 225
  38. 38.What is the distance between the points (6, 2) and (12, 10)? (a) 14 (b) 100 (c) 11 (d) 10
  39. 39.What is the distance between the points (3, 7) and (11, 13)? (a) 100 (b) 11 (c) 10 (d) 14
  40. 40.What is the midpoint of the line joining (10, 7) and (18, 13)? (a) (10, 14) (b) (28, 20) (c) (4, 3) (d) (14, 10)

Answer key

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

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