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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 543 · 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.How far is the point (16, 12) from the origin (0, 0)? (a) 400 (b) 20 (c) 28 (d) 21
  2. 2.What is the distance between the points (8, 6) and (14, 14)? (a) 11 (b) 14 (c) 10 (d) 100
  3. 3.How far is the point (12, 5) from the origin (0, 0)? (a) 169 (b) 17 (c) 14 (d) 13
  4. 4.What is the distance between the points (4, 12) and (19, 4)? (a) 23 (b) 289 (c) 17 (d) 18
  5. 5.What is the midpoint of the line joining (7, 18) and (17, 8)? (a) (5, 5) (b) (13, 12) (c) (24, 26) (d) (12, 13)
  6. 6.In which quadrant does the point (−1, 1) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  7. 7.What is the midpoint of the line joining (0, 6) and (10, 8)? (a) (7, 5) (b) (5, 1) (c) (10, 14) (d) (5, 7)
  8. 8.What is the distance between the points (2, 1) and (14, 17)? (a) 20 (b) 28 (c) 400 (d) 21
  9. 9.How far is the point (8, 6) from the origin (0, 0)? (a) 14 (b) 100 (c) 11 (d) 10
  10. 10.How far is the point (12, 9) from the origin (0, 0)? (a) 21 (b) 16 (c) 225 (d) 15
  11. 11.What is the midpoint of the line joining (3, 7) and (9, 9)? (a) (6, 8) (b) (3, 1) (c) (12, 16) (d) (8, 6)
  12. 12.In which quadrant does the point (−4, 8) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
  13. 13.How far is the point (6, 8) from the origin (0, 0)? (a) 10 (b) 100 (c) 11 (d) 14
  14. 14.In which quadrant does the point (2, −5) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  15. 15.What is the distance between the points (1, 7) and (13, 16)? (a) 225 (b) 16 (c) 15 (d) 21
  16. 16.In which quadrant does the point (2, 3) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  17. 17.What is the distance between the points (7, 9) and (16, 21)? (a) 225 (b) 15 (c) 16 (d) 21
  18. 18.What is the distance between the points (3, 12) and (15, 7)? (a) 169 (b) 13 (c) 17 (d) 14
  19. 19.What is the distance between the points (4, 14) and (16, 9)? (a) 17 (b) 14 (c) 13 (d) 169
  20. 20.How far is the point (15, 8) from the origin (0, 0)? (a) 23 (b) 18 (c) 289 (d) 17
  21. 21.How far is the point (3, 4) from the origin (0, 0)? (a) 6 (b) 5 (c) 25 (d) 7
  22. 22.How far is the point (8, 15) from the origin (0, 0)? (a) 23 (b) 18 (c) 289 (d) 17
  23. 23.What is the distance between the points (4, 3) and (19, 11)? (a) 23 (b) 18 (c) 289 (d) 17
  24. 24.What is the distance between the points (6, 8) and (14, 2)? (a) 11 (b) 10 (c) 100 (d) 14
  25. 25.What is the distance between the points (5, 9) and (20, 1)? (a) 23 (b) 18 (c) 17 (d) 289
  26. 26.In which quadrant does the point (9, 4) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  27. 27.What is the midpoint of the line joining (4, 1) and (8, 3)? (a) (6, 2) (b) (2, 6) (c) (12, 4) (d) (2, 1)
  28. 28.How far is the point (4, 3) from the origin (0, 0)? (a) 5 (b) 7 (c) 6 (d) 25
  29. 29.What is the distance between the points (1, 9) and (4, 5)? (a) 25 (b) 5 (c) 6 (d) 7
  30. 30.What is the distance between the points (2, 7) and (14, 2)? (a) 17 (b) 169 (c) 14 (d) 13
  31. 31.In which quadrant does the point (9, 9) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  32. 32.How far is the point (12, 16) from the origin (0, 0)? (a) 28 (b) 21 (c) 400 (d) 20
  33. 33.How far is the point (7, 24) from the origin (0, 0)? (a) 26 (b) 25 (c) 31 (d) 625
  34. 34.How far is the point (5, 12) from the origin (0, 0)? (a) 17 (b) 13 (c) 14 (d) 169
  35. 35.What is the midpoint of the line joining (4, 6) and (14, 18)? (a) (12, 9) (b) (9, 12) (c) (18, 24) (d) (5, 6)
  36. 36.What is the distance between the points (0, 11) and (12, 6)? (a) 13 (b) 169 (c) 14 (d) 17
  37. 37.What is the midpoint of the line joining (5, 12) and (11, 6)? (a) (16, 18) (b) (9, 8) (c) (3, 3) (d) (8, 9)
  38. 38.What is the distance between the points (5, 8) and (21, 20)? (a) 20 (b) 28 (c) 21 (d) 400
  39. 39.What is the distance between the points (0, 22) and (12, 6)? (a) 20 (b) 400 (c) 28 (d) 21
  40. 40.What is the midpoint of the line joining (8, 2) and (10, 12)? (a) (7, 9) (b) (1, 5) (c) (9, 7) (d) (18, 14)

Answer key

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

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