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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 493 · 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 midpoint of the line joining (1, 16) and (11, 10)? (a) (13, 6) (b) (6, 13) (c) (12, 26) (d) (5, 3)
  2. 2.In which quadrant does the point (3, 6) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  3. 3.What is the midpoint of the line joining (2, 9) and (14, 1)? (a) (5, 8) (b) (6, 4) (c) (16, 10) (d) (8, 5)
  4. 4.In which quadrant does the point (8, 8) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  5. 5.What is the distance between the points (3, 3) and (11, 18)? (a) 289 (b) 18 (c) 17 (d) 23
  6. 6.What is the distance between the points (1, 5) and (9, 11)? (a) 11 (b) 14 (c) 100 (d) 10
  7. 7.In which quadrant does the point (−8, −5) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
  8. 8.What is the distance between the points (2, 7) and (14, 23)? (a) 400 (b) 28 (c) 21 (d) 20
  9. 9.What is the distance between the points (1, 18) and (13, 9)? (a) 21 (b) 15 (c) 225 (d) 16
  10. 10.What is the midpoint of the line joining (10, 9) and (20, 21)? (a) (15, 15) (b) (5, 6) (c) (30, 30) (d) (16, 15)
  11. 11.What is the distance between the points (3, 7) and (7, 4)? (a) 5 (b) 6 (c) 7 (d) 25
  12. 12.What is the distance between the points (5, 8) and (14, 20)? (a) 16 (b) 21 (c) 225 (d) 15
  13. 13.In which quadrant does the point (−8, 7) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  14. 14.What is the distance between the points (3, 4) and (7, 7)? (a) 25 (b) 7 (c) 5 (d) 6
  15. 15.What is the distance between the points (5, 9) and (17, 25)? (a) 400 (b) 28 (c) 20 (d) 21
  16. 16.In which quadrant does the point (−9, 1) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  17. 17.How far is the point (5, 12) from the origin (0, 0)? (a) 14 (b) 17 (c) 169 (d) 13
  18. 18.What is the distance between the points (9, 2) and (24, 10)? (a) 18 (b) 23 (c) 289 (d) 17
  19. 19.What is the distance between the points (2, 21) and (18, 9)? (a) 28 (b) 20 (c) 400 (d) 21
  20. 20.What is the midpoint of the line joining (5, 8) and (17, 6)? (a) (7, 11) (b) (22, 14) (c) (11, 7) (d) (6, 1)
  21. 21.What is the distance between the points (9, 8) and (12, 12)? (a) 6 (b) 25 (c) 5 (d) 7
  22. 22.What is the midpoint of the line joining (5, 13) and (9, 5)? (a) (7, 9) (b) (9, 7) (c) (14, 18) (d) (2, 4)
  23. 23.What is the distance between the points (7, 13) and (23, 1)? (a) 20 (b) 28 (c) 21 (d) 400
  24. 24.What is the midpoint of the line joining (0, 2) and (2, 0)? (a) (1, 1) (b) (1, 2) (c) (2, 1) (d) (2, 2)
  25. 25.How far is the point (3, 4) from the origin (0, 0)? (a) 6 (b) 25 (c) 7 (d) 5
  26. 26.How far is the point (4, 3) from the origin (0, 0)? (a) 5 (b) 7 (c) 25 (d) 6
  27. 27.What is the midpoint of the line joining (0, 0) and (6, 2)? (a) (6, 2) (b) (4, 1) (c) (1, 3) (d) (3, 1)
  28. 28.What is the midpoint of the line joining (3, 2) and (7, 6)? (a) (10, 8) (b) (5, 4) (c) (2, 2) (d) (4, 5)
  29. 29.What is the midpoint of the line joining (2, 16) and (10, 10)? (a) (6, 13) (b) (12, 26) (c) (13, 6) (d) (4, 3)
  30. 30.How far is the point (16, 12) from the origin (0, 0)? (a) 400 (b) 28 (c) 21 (d) 20
  31. 31.What is the distance between the points (9, 5) and (12, 1)? (a) 6 (b) 25 (c) 5 (d) 7
  32. 32.What is the midpoint of the line joining (7, 12) and (15, 4)? (a) (22, 16) (b) (8, 11) (c) (11, 8) (d) (4, 4)
  33. 33.What is the midpoint of the line joining (8, 9) and (12, 15)? (a) (10, 12) (b) (20, 24) (c) (12, 10) (d) (2, 3)
  34. 34.What is the distance between the points (1, 4) and (9, 19)? (a) 289 (b) 17 (c) 23 (d) 18
  35. 35.In which quadrant does the point (2, 9) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  36. 36.What is the midpoint of the line joining (9, 3) and (13, 9)? (a) (22, 12) (b) (11, 6) (c) (2, 3) (d) (6, 11)
  37. 37.What is the midpoint of the line joining (3, 5) and (15, 3)? (a) (6, 1) (b) (4, 9) (c) (18, 8) (d) (9, 4)
  38. 38.What is the distance between the points (8, 7) and (17, 19)? (a) 225 (b) 16 (c) 15 (d) 21
  39. 39.In which quadrant does the point (9, 2) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  40. 40.What is the distance between the points (6, 5) and (14, 11)? (a) 100 (b) 11 (c) 10 (d) 14

Answer key

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

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