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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 241 · 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 (2, 9) and (17, 1)? (a) 17 (b) 18 (c) 23 (d) 289
  2. 2.What is the distance between the points (4, 8) and (20, 20)? (a) 28 (b) 20 (c) 21 (d) 400
  3. 3.What is the distance between the points (2, 6) and (14, 11)? (a) 13 (b) 169 (c) 17 (d) 14
  4. 4.What is the midpoint of the line joining (7, 3) and (13, 1)? (a) (2, 10) (b) (20, 4) (c) (10, 2) (d) (3, 1)
  5. 5.How far is the point (9, 12) from the origin (0, 0)? (a) 16 (b) 15 (c) 21 (d) 225
  6. 6.How far is the point (7, 24) from the origin (0, 0)? (a) 25 (b) 625 (c) 31 (d) 26
  7. 7.What is the distance between the points (9, 0) and (21, 16)? (a) 21 (b) 28 (c) 400 (d) 20
  8. 8.What is the distance between the points (0, 9) and (3, 5)? (a) 7 (b) 6 (c) 5 (d) 25
  9. 9.What is the distance between the points (2, 11) and (8, 3)? (a) 10 (b) 100 (c) 14 (d) 11
  10. 10.What is the midpoint of the line joining (0, 10) and (4, 2)? (a) (6, 2) (b) (2, 6) (c) (4, 12) (d) (2, 4)
  11. 11.In which quadrant does the point (7, 8) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  12. 12.What is the midpoint of the line joining (4, 10) and (14, 20)? (a) (15, 9) (b) (9, 15) (c) (5, 5) (d) (18, 30)
  13. 13.What is the distance between the points (0, 13) and (15, 5)? (a) 23 (b) 17 (c) 18 (d) 289
  14. 14.How far is the point (12, 5) from the origin (0, 0)? (a) 17 (b) 169 (c) 14 (d) 13
  15. 15.What is the midpoint of the line joining (10, 9) and (16, 5)? (a) (7, 13) (b) (13, 7) (c) (3, 2) (d) (26, 14)
  16. 16.What is the midpoint of the line joining (6, 14) and (10, 2)? (a) (9, 8) (b) (16, 16) (c) (8, 8) (d) (2, 6)
  17. 17.What is the distance between the points (0, 24) and (8, 9)? (a) 18 (b) 17 (c) 289 (d) 23
  18. 18.In which quadrant does the point (7, 3) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  19. 19.How far is the point (4, 3) from the origin (0, 0)? (a) 25 (b) 5 (c) 7 (d) 6
  20. 20.How far is the point (16, 12) from the origin (0, 0)? (a) 400 (b) 20 (c) 21 (d) 28
  21. 21.What is the distance between the points (4, 11) and (10, 3)? (a) 11 (b) 10 (c) 100 (d) 14
  22. 22.What is the midpoint of the line joining (9, 0) and (17, 2)? (a) (1, 13) (b) (13, 1) (c) (26, 2) (d) (4, 1)
  23. 23.In which quadrant does the point (−5, 3) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  24. 24.What is the distance between the points (3, 21) and (15, 5)? (a) 21 (b) 20 (c) 400 (d) 28
  25. 25.What is the distance between the points (2, 1) and (9, 25)? (a) 25 (b) 625 (c) 31 (d) 26
  26. 26.What is the midpoint of the line joining (8, 7) and (12, 19)? (a) (13, 10) (b) (2, 6) (c) (20, 26) (d) (10, 13)
  27. 27.How far is the point (8, 15) from the origin (0, 0)? (a) 17 (b) 289 (c) 23 (d) 18
  28. 28.What is the distance between the points (1, 12) and (13, 3)? (a) 21 (b) 16 (c) 225 (d) 15
  29. 29.How far is the point (6, 8) from the origin (0, 0)? (a) 100 (b) 10 (c) 14 (d) 11
  30. 30.How far is the point (5, 12) from the origin (0, 0)? (a) 169 (b) 13 (c) 14 (d) 17
  31. 31.How far is the point (12, 9) from the origin (0, 0)? (a) 15 (b) 225 (c) 16 (d) 21
  32. 32.In which quadrant does the point (8, −5) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  33. 33.What is the distance between the points (1, 8) and (7, 16)? (a) 100 (b) 11 (c) 14 (d) 10
  34. 34.In which quadrant does the point (2, −5) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  35. 35.What is the distance between the points (9, 3) and (25, 15)? (a) 21 (b) 400 (c) 28 (d) 20
  36. 36.What is the distance between the points (5, 7) and (12, 31)? (a) 625 (b) 31 (c) 26 (d) 25
  37. 37.What is the distance between the points (2, 9) and (10, 3)? (a) 14 (b) 10 (c) 100 (d) 11
  38. 38.In which quadrant does the point (−4, −9) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  39. 39.What is the midpoint of the line joining (9, 17) and (21, 5)? (a) (6, 6) (b) (11, 15) (c) (30, 22) (d) (15, 11)
  40. 40.What is the midpoint of the line joining (6, 1) and (18, 11)? (a) (6, 12) (b) (6, 5) (c) (24, 12) (d) (12, 6)

Answer key

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

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