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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 778 · 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 (2, 9) and (10, 15)? (a) (12, 6) (b) (4, 3) (c) (6, 12) (d) (12, 24)
  2. 2.How far is the point (12, 16) from the origin (0, 0)? (a) 21 (b) 20 (c) 28 (d) 400
  3. 3.What is the distance between the points (9, 19) and (14, 7)? (a) 13 (b) 17 (c) 169 (d) 14
  4. 4.What is the midpoint of the line joining (3, 6) and (7, 0)? (a) (3, 5) (b) (2, 3) (c) (10, 6) (d) (5, 3)
  5. 5.What is the midpoint of the line joining (0, 9) and (6, 11)? (a) (3, 1) (b) (10, 3) (c) (3, 10) (d) (6, 20)
  6. 6.In which quadrant does the point (1, 9) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  7. 7.How far is the point (6, 8) from the origin (0, 0)? (a) 14 (b) 10 (c) 100 (d) 11
  8. 8.What is the distance between the points (5, 5) and (21, 17)? (a) 28 (b) 400 (c) 20 (d) 21
  9. 9.What is the midpoint of the line joining (3, 9) and (11, 13)? (a) (14, 22) (b) (7, 11) (c) (4, 2) (d) (11, 7)
  10. 10.What is the distance between the points (6, 3) and (18, 8)? (a) 169 (b) 17 (c) 13 (d) 14
  11. 11.What is the midpoint of the line joining (9, 18) and (19, 8)? (a) (5, 5) (b) (14, 13) (c) (28, 26) (d) (13, 14)
  12. 12.How far is the point (3, 4) from the origin (0, 0)? (a) 6 (b) 25 (c) 5 (d) 7
  13. 13.What is the distance between the points (9, 3) and (25, 15)? (a) 21 (b) 28 (c) 20 (d) 400
  14. 14.What is the distance between the points (6, 1) and (11, 13)? (a) 17 (b) 13 (c) 169 (d) 14
  15. 15.In which quadrant does the point (3, 8) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  16. 16.How far is the point (8, 6) from the origin (0, 0)? (a) 10 (b) 100 (c) 11 (d) 14
  17. 17.What is the midpoint of the line joining (0, 3) and (6, 13)? (a) (6, 16) (b) (8, 3) (c) (3, 5) (d) (3, 8)
  18. 18.In which quadrant does the point (4, −7) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  19. 19.What is the distance between the points (3, 8) and (6, 4)? (a) 7 (b) 6 (c) 5 (d) 25
  20. 20.What is the midpoint of the line joining (2, 8) and (14, 4)? (a) (6, 2) (b) (16, 12) (c) (6, 8) (d) (8, 6)
  21. 21.What is the midpoint of the line joining (2, 3) and (10, 9)? (a) (6, 6) (b) (12, 12) (c) (4, 3) (d) (7, 6)
  22. 22.What is the midpoint of the line joining (9, 5) and (19, 17)? (a) (11, 14) (b) (5, 6) (c) (28, 22) (d) (14, 11)
  23. 23.What is the distance between the points (6, 0) and (18, 16)? (a) 21 (b) 20 (c) 28 (d) 400
  24. 24.What is the midpoint of the line joining (7, 5) and (13, 1)? (a) (3, 2) (b) (20, 6) (c) (3, 10) (d) (10, 3)
  25. 25.In which quadrant does the point (2, 4) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  26. 26.What is the midpoint of the line joining (2, 3) and (10, 1)? (a) (6, 2) (b) (4, 1) (c) (2, 6) (d) (12, 4)
  27. 27.What is the distance between the points (4, 0) and (16, 9)? (a) 225 (b) 21 (c) 16 (d) 15
  28. 28.What is the midpoint of the line joining (8, 10) and (18, 8)? (a) (26, 18) (b) (9, 13) (c) (5, 1) (d) (13, 9)
  29. 29.What is the midpoint of the line joining (6, 0) and (8, 4)? (a) (2, 7) (b) (7, 2) (c) (1, 2) (d) (14, 4)
  30. 30.How far is the point (12, 9) from the origin (0, 0)? (a) 16 (b) 21 (c) 225 (d) 15
  31. 31.What is the midpoint of the line joining (1, 4) and (11, 2)? (a) (6, 3) (b) (3, 6) (c) (12, 6) (d) (5, 1)
  32. 32.What is the midpoint of the line joining (1, 9) and (9, 1)? (a) (10, 10) (b) (6, 5) (c) (4, 4) (d) (5, 5)
  33. 33.What is the distance between the points (0, 3) and (6, 11)? (a) 14 (b) 100 (c) 10 (d) 11
  34. 34.What is the distance between the points (3, 5) and (15, 0)? (a) 14 (b) 17 (c) 169 (d) 13
  35. 35.What is the distance between the points (2, 4) and (5, 0)? (a) 6 (b) 7 (c) 25 (d) 5
  36. 36.What is the distance between the points (0, 3) and (12, 12)? (a) 21 (b) 16 (c) 225 (d) 15
  37. 37.What is the distance between the points (1, 2) and (9, 8)? (a) 100 (b) 11 (c) 10 (d) 14
  38. 38.How far is the point (24, 7) from the origin (0, 0)? (a) 26 (b) 625 (c) 31 (d) 25
  39. 39.How far is the point (8, 15) from the origin (0, 0)? (a) 17 (b) 23 (c) 289 (d) 18
  40. 40.What is the distance between the points (3, 3) and (7, 6)? (a) 25 (b) 7 (c) 5 (d) 6

Answer key

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

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