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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 353 · 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 (1, 15) and (16, 7)? (a) 23 (b) 289 (c) 18 (d) 17
  2. 2.In which quadrant does the point (−6, 6) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  3. 3.What is the midpoint of the line joining (1, 5) and (3, 11)? (a) (8, 2) (b) (2, 8) (c) (4, 16) (d) (1, 3)
  4. 4.What is the distance between the points (3, 8) and (10, 32)? (a) 31 (b) 625 (c) 26 (d) 25
  5. 5.In which quadrant does the point (3, 5) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  6. 6.How far is the point (4, 3) from the origin (0, 0)? (a) 7 (b) 25 (c) 6 (d) 5
  7. 7.What is the midpoint of the line joining (7, 16) and (19, 4)? (a) (26, 20) (b) (10, 13) (c) (6, 6) (d) (13, 10)
  8. 8.What is the distance between the points (0, 0) and (12, 9)? (a) 225 (b) 21 (c) 15 (d) 16
  9. 9.What is the distance between the points (3, 2) and (15, 7)? (a) 17 (b) 14 (c) 13 (d) 169
  10. 10.How far is the point (12, 16) from the origin (0, 0)? (a) 20 (b) 28 (c) 21 (d) 400
  11. 11.What is the distance between the points (9, 7) and (12, 11)? (a) 6 (b) 5 (c) 25 (d) 7
  12. 12.What is the midpoint of the line joining (3, 8) and (13, 4)? (a) (5, 2) (b) (6, 8) (c) (16, 12) (d) (8, 6)
  13. 13.How far is the point (5, 12) from the origin (0, 0)? (a) 14 (b) 17 (c) 169 (d) 13
  14. 14.How far is the point (24, 7) from the origin (0, 0)? (a) 31 (b) 625 (c) 25 (d) 26
  15. 15.What is the distance between the points (2, 15) and (18, 3)? (a) 21 (b) 400 (c) 20 (d) 28
  16. 16.What is the distance between the points (0, 9) and (3, 13)? (a) 6 (b) 25 (c) 5 (d) 7
  17. 17.What is the distance between the points (5, 8) and (10, 20)? (a) 14 (b) 169 (c) 13 (d) 17
  18. 18.What is the midpoint of the line joining (10, 16) and (20, 8)? (a) (15, 12) (b) (30, 24) (c) (5, 4) (d) (12, 15)
  19. 19.What is the distance between the points (7, 15) and (31, 8)? (a) 31 (b) 26 (c) 25 (d) 625
  20. 20.What is the distance between the points (6, 0) and (9, 4)? (a) 6 (b) 25 (c) 5 (d) 7
  21. 21.In which quadrant does the point (2, 1) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  22. 22.How far is the point (8, 15) from the origin (0, 0)? (a) 17 (b) 18 (c) 289 (d) 23
  23. 23.What is the distance between the points (6, 2) and (30, 9)? (a) 625 (b) 31 (c) 25 (d) 26
  24. 24.What is the midpoint of the line joining (0, 2) and (8, 4)? (a) (4, 1) (b) (4, 3) (c) (8, 6) (d) (3, 4)
  25. 25.How far is the point (12, 5) from the origin (0, 0)? (a) 169 (b) 13 (c) 14 (d) 17
  26. 26.What is the midpoint of the line joining (6, 17) and (8, 9)? (a) (14, 26) (b) (13, 7) (c) (1, 4) (d) (7, 13)
  27. 27.What is the midpoint of the line joining (1, 3) and (9, 15)? (a) (10, 18) (b) (5, 9) (c) (4, 6) (d) (9, 5)
  28. 28.What is the distance between the points (2, 14) and (14, 5)? (a) 225 (b) 15 (c) 21 (d) 16
  29. 29.What is the midpoint of the line joining (5, 13) and (17, 1)? (a) (6, 6) (b) (11, 7) (c) (22, 14) (d) (7, 11)
  30. 30.How far is the point (15, 8) from the origin (0, 0)? (a) 23 (b) 17 (c) 289 (d) 18
  31. 31.What is the midpoint of the line joining (9, 5) and (11, 9)? (a) (20, 14) (b) (10, 7) (c) (7, 10) (d) (1, 2)
  32. 32.What is the midpoint of the line joining (2, 4) and (14, 6)? (a) (5, 8) (b) (6, 1) (c) (16, 10) (d) (8, 5)
  33. 33.In which quadrant does the point (4, 2) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  34. 34.What is the distance between the points (8, 3) and (23, 11)? (a) 17 (b) 23 (c) 289 (d) 18
  35. 35.In which quadrant does the point (−2, 9) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  36. 36.What is the midpoint of the line joining (1, 20) and (13, 10)? (a) (15, 7) (b) (14, 30) (c) (6, 5) (d) (7, 15)
  37. 37.What is the distance between the points (4, 6) and (20, 18)? (a) 21 (b) 400 (c) 20 (d) 28
  38. 38.What is the midpoint of the line joining (2, 12) and (8, 6)? (a) (5, 9) (b) (10, 18) (c) (9, 5) (d) (3, 3)
  39. 39.In which quadrant does the point (7, 9) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  40. 40.What is the distance between the points (9, 17) and (25, 5)? (a) 28 (b) 400 (c) 20 (d) 21

Answer key

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

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