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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 841 · 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 (7, 4) and (15, 10)? (a) 10 (b) 11 (c) 100 (d) 14
  2. 2.What is the distance between the points (7, 9) and (19, 0)? (a) 16 (b) 225 (c) 15 (d) 21
  3. 3.What is the midpoint of the line joining (2, 17) and (14, 7)? (a) (6, 5) (b) (16, 24) (c) (8, 12) (d) (12, 8)
  4. 4.What is the midpoint of the line joining (6, 16) and (16, 10)? (a) (5, 3) (b) (13, 11) (c) (22, 26) (d) (11, 13)
  5. 5.What is the midpoint of the line joining (10, 19) and (20, 9)? (a) (5, 5) (b) (30, 28) (c) (15, 14) (d) (14, 15)
  6. 6.What is the distance between the points (4, 9) and (20, 21)? (a) 400 (b) 20 (c) 28 (d) 21
  7. 7.In which quadrant does the point (2, −1) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  8. 8.What is the distance between the points (7, 9) and (23, 21)? (a) 28 (b) 400 (c) 20 (d) 21
  9. 9.In which quadrant does the point (5, 1) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  10. 10.What is the distance between the points (2, 3) and (5, 7)? (a) 7 (b) 25 (c) 6 (d) 5
  11. 11.What is the midpoint of the line joining (3, 6) and (15, 14)? (a) (6, 4) (b) (18, 20) (c) (10, 9) (d) (9, 10)
  12. 12.What is the midpoint of the line joining (6, 10) and (8, 0)? (a) (1, 5) (b) (14, 10) (c) (7, 5) (d) (5, 7)
  13. 13.In which quadrant does the point (7, −2) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  14. 14.What is the distance between the points (4, 3) and (7, 7)? (a) 7 (b) 5 (c) 6 (d) 25
  15. 15.What is the midpoint of the line joining (6, 12) and (12, 4)? (a) (18, 16) (b) (8, 9) (c) (9, 8) (d) (3, 4)
  16. 16.What is the midpoint of the line joining (3, 2) and (7, 12)? (a) (7, 5) (b) (2, 5) (c) (10, 14) (d) (5, 7)
  17. 17.What is the distance between the points (6, 13) and (18, 4)? (a) 225 (b) 15 (c) 21 (d) 16
  18. 18.What is the midpoint of the line joining (2, 8) and (12, 2)? (a) (14, 10) (b) (7, 5) (c) (5, 7) (d) (5, 3)
  19. 19.What is the distance between the points (0, 2) and (12, 18)? (a) 28 (b) 21 (c) 400 (d) 20
  20. 20.In which quadrant does the point (4, 9) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  21. 21.In which quadrant does the point (−5, 8) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  22. 22.What is the midpoint of the line joining (9, 12) and (17, 8)? (a) (10, 13) (b) (13, 10) (c) (26, 20) (d) (4, 2)
  23. 23.What is the distance between the points (4, 10) and (28, 3)? (a) 26 (b) 25 (c) 31 (d) 625
  24. 24.What is the midpoint of the line joining (10, 5) and (22, 15)? (a) (32, 20) (b) (10, 16) (c) (6, 5) (d) (16, 10)
  25. 25.What is the distance between the points (4, 3) and (8, 6)? (a) 5 (b) 7 (c) 25 (d) 6
  26. 26.What is the distance between the points (2, 6) and (5, 2)? (a) 6 (b) 5 (c) 7 (d) 25
  27. 27.In which quadrant does the point (6, −4) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  28. 28.What is the midpoint of the line joining (7, 10) and (11, 8)? (a) (10, 9) (b) (9, 9) (c) (2, 1) (d) (18, 18)
  29. 29.How far is the point (12, 16) from the origin (0, 0)? (a) 400 (b) 28 (c) 20 (d) 21
  30. 30.How far is the point (9, 12) from the origin (0, 0)? (a) 21 (b) 15 (c) 225 (d) 16
  31. 31.How far is the point (8, 6) from the origin (0, 0)? (a) 10 (b) 11 (c) 14 (d) 100
  32. 32.What is the midpoint of the line joining (8, 1) and (20, 11)? (a) (6, 14) (b) (28, 12) (c) (6, 5) (d) (14, 6)
  33. 33.What is the distance between the points (9, 13) and (21, 8)? (a) 14 (b) 169 (c) 17 (d) 13
  34. 34.What is the distance between the points (9, 8) and (25, 20)? (a) 400 (b) 21 (c) 28 (d) 20
  35. 35.What is the distance between the points (8, 7) and (32, 0)? (a) 25 (b) 31 (c) 625 (d) 26
  36. 36.What is the midpoint of the line joining (3, 5) and (7, 9)? (a) (5, 7) (b) (10, 14) (c) (2, 2) (d) (7, 5)
  37. 37.How far is the point (3, 4) from the origin (0, 0)? (a) 25 (b) 5 (c) 6 (d) 7
  38. 38.What is the midpoint of the line joining (5, 10) and (9, 6)? (a) (2, 2) (b) (14, 16) (c) (7, 8) (d) (8, 7)
  39. 39.How far is the point (6, 8) from the origin (0, 0)? (a) 14 (b) 100 (c) 10 (d) 11
  40. 40.What is the distance between the points (9, 7) and (17, 1)? (a) 100 (b) 14 (c) 10 (d) 11

Answer key

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

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