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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 207 · 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 (8, 9) and (24, 21)? (a) 21 (b) 28 (c) 20 (d) 400
  2. 2.What is the midpoint of the line joining (8, 3) and (12, 1)? (a) (20, 4) (b) (2, 1) (c) (2, 10) (d) (10, 2)
  3. 3.In which quadrant does the point (7, −2) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  4. 4.What is the midpoint of the line joining (0, 21) and (10, 9)? (a) (15, 5) (b) (5, 6) (c) (10, 30) (d) (5, 15)
  5. 5.What is the midpoint of the line joining (4, 10) and (6, 20)? (a) (15, 5) (b) (1, 5) (c) (10, 30) (d) (5, 15)
  6. 6.What is the midpoint of the line joining (3, 8) and (5, 16)? (a) (1, 4) (b) (8, 24) (c) (12, 4) (d) (4, 12)
  7. 7.In which quadrant does the point (−6, 9) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  8. 8.What is the midpoint of the line joining (5, 12) and (15, 4)? (a) (8, 10) (b) (20, 16) (c) (10, 8) (d) (5, 4)
  9. 9.In which quadrant does the point (−7, −4) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  10. 10.How far is the point (9, 12) from the origin (0, 0)? (a) 16 (b) 21 (c) 15 (d) 225
  11. 11.How far is the point (4, 3) from the origin (0, 0)? (a) 7 (b) 5 (c) 25 (d) 6
  12. 12.What is the midpoint of the line joining (2, 20) and (14, 10)? (a) (6, 5) (b) (15, 8) (c) (16, 30) (d) (8, 15)
  13. 13.What is the distance between the points (0, 15) and (9, 3)? (a) 225 (b) 21 (c) 15 (d) 16
  14. 14.What is the distance between the points (6, 2) and (21, 10)? (a) 17 (b) 23 (c) 289 (d) 18
  15. 15.What is the distance between the points (2, 9) and (14, 18)? (a) 21 (b) 225 (c) 15 (d) 16
  16. 16.In which quadrant does the point (−6, −4) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  17. 17.What is the midpoint of the line joining (8, 0) and (16, 8)? (a) (4, 12) (b) (24, 8) (c) (4, 4) (d) (12, 4)
  18. 18.What is the midpoint of the line joining (6, 16) and (18, 6)? (a) (6, 5) (b) (11, 12) (c) (24, 22) (d) (12, 11)
  19. 19.What is the midpoint of the line joining (8, 10) and (10, 16)? (a) (13, 9) (b) (9, 13) (c) (1, 3) (d) (18, 26)
  20. 20.What is the midpoint of the line joining (8, 1) and (10, 3)? (a) (18, 4) (b) (1, 1) (c) (2, 9) (d) (9, 2)
  21. 21.What is the distance between the points (7, 12) and (12, 0)? (a) 14 (b) 13 (c) 17 (d) 169
  22. 22.What is the distance between the points (2, 10) and (10, 4)? (a) 11 (b) 14 (c) 10 (d) 100
  23. 23.What is the midpoint of the line joining (5, 8) and (15, 0)? (a) (10, 4) (b) (5, 4) (c) (4, 10) (d) (20, 8)
  24. 24.What is the distance between the points (3, 2) and (11, 8)? (a) 11 (b) 10 (c) 14 (d) 100
  25. 25.How far is the point (12, 5) from the origin (0, 0)? (a) 17 (b) 169 (c) 14 (d) 13
  26. 26.What is the midpoint of the line joining (7, 11) and (9, 7)? (a) (1, 2) (b) (9, 8) (c) (16, 18) (d) (8, 9)
  27. 27.How far is the point (8, 15) from the origin (0, 0)? (a) 23 (b) 17 (c) 289 (d) 18
  28. 28.What is the midpoint of the line joining (10, 6) and (18, 8)? (a) (28, 14) (b) (4, 1) (c) (7, 14) (d) (14, 7)
  29. 29.How far is the point (12, 16) from the origin (0, 0)? (a) 28 (b) 21 (c) 400 (d) 20
  30. 30.What is the distance between the points (1, 2) and (25, 9)? (a) 31 (b) 26 (c) 25 (d) 625
  31. 31.What is the midpoint of the line joining (2, 15) and (8, 9)? (a) (10, 24) (b) (3, 3) (c) (12, 5) (d) (5, 12)
  32. 32.In which quadrant does the point (2, 8) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  33. 33.What is the distance between the points (4, 3) and (7, 7)? (a) 6 (b) 7 (c) 5 (d) 25
  34. 34.What is the distance between the points (9, 8) and (17, 14)? (a) 10 (b) 100 (c) 14 (d) 11
  35. 35.In which quadrant does the point (4, 5) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  36. 36.What is the midpoint of the line joining (10, 10) and (12, 6)? (a) (1, 2) (b) (11, 8) (c) (22, 16) (d) (8, 11)
  37. 37.In which quadrant does the point (5, 5) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  38. 38.What is the distance between the points (4, 0) and (8, 3)? (a) 7 (b) 5 (c) 6 (d) 25
  39. 39.How far is the point (15, 8) from the origin (0, 0)? (a) 18 (b) 289 (c) 17 (d) 23
  40. 40.What is the distance between the points (3, 19) and (15, 3)? (a) 21 (b) 400 (c) 28 (d) 20

Answer key

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

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