← Coordinates and distance lesson New set →

Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 668 · 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, 17) and (7, 5)? (a) 17 (b) 14 (c) 169 (d) 13
  2. 2.What is the distance between the points (8, 7) and (16, 22)? (a) 18 (b) 23 (c) 17 (d) 289
  3. 3.What is the midpoint of the line joining (1, 22) and (11, 10)? (a) (5, 6) (b) (12, 32) (c) (6, 16) (d) (16, 6)
  4. 4.What is the distance between the points (1, 2) and (13, 18)? (a) 400 (b) 20 (c) 21 (d) 28
  5. 5.What is the midpoint of the line joining (3, 1) and (13, 3)? (a) (8, 2) (b) (5, 1) (c) (16, 4) (d) (2, 8)
  6. 6.What is the distance between the points (3, 1) and (27, 8)? (a) 26 (b) 31 (c) 25 (d) 625
  7. 7.What is the midpoint of the line joining (8, 9) and (16, 5)? (a) (7, 12) (b) (4, 2) (c) (12, 7) (d) (24, 14)
  8. 8.In which quadrant does the point (−2, 4) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  9. 9.What is the midpoint of the line joining (8, 3) and (10, 9)? (a) (18, 12) (b) (6, 9) (c) (9, 6) (d) (1, 3)
  10. 10.In which quadrant does the point (−8, 9) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  11. 11.What is the midpoint of the line joining (2, 5) and (4, 1)? (a) (4, 3) (b) (1, 2) (c) (3, 3) (d) (6, 6)
  12. 12.What is the distance between the points (9, 8) and (15, 0)? (a) 10 (b) 100 (c) 11 (d) 14
  13. 13.What is the distance between the points (2, 4) and (6, 7)? (a) 25 (b) 6 (c) 5 (d) 7
  14. 14.What is the distance between the points (9, 7) and (12, 11)? (a) 25 (b) 6 (c) 7 (d) 5
  15. 15.In which quadrant does the point (−4, 7) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  16. 16.What is the midpoint of the line joining (9, 6) and (11, 12)? (a) (1, 3) (b) (9, 10) (c) (20, 18) (d) (10, 9)
  17. 17.What is the distance between the points (9, 15) and (17, 0)? (a) 289 (b) 18 (c) 23 (d) 17
  18. 18.How far is the point (5, 12) from the origin (0, 0)? (a) 14 (b) 17 (c) 13 (d) 169
  19. 19.How far is the point (12, 5) from the origin (0, 0)? (a) 14 (b) 169 (c) 17 (d) 13
  20. 20.What is the distance between the points (6, 25) and (13, 1)? (a) 26 (b) 625 (c) 25 (d) 31
  21. 21.What is the midpoint of the line joining (10, 5) and (14, 7)? (a) (6, 12) (b) (2, 1) (c) (12, 6) (d) (24, 12)
  22. 22.How far is the point (7, 24) from the origin (0, 0)? (a) 625 (b) 25 (c) 31 (d) 26
  23. 23.What is the distance between the points (4, 18) and (9, 6)? (a) 17 (b) 14 (c) 13 (d) 169
  24. 24.What is the distance between the points (1, 20) and (13, 4)? (a) 21 (b) 20 (c) 28 (d) 400
  25. 25.In which quadrant does the point (2, −9) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  26. 26.What is the distance between the points (7, 30) and (14, 6)? (a) 25 (b) 31 (c) 625 (d) 26
  27. 27.In which quadrant does the point (−5, −9) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
  28. 28.What is the distance between the points (8, 27) and (15, 3)? (a) 31 (b) 625 (c) 26 (d) 25
  29. 29.How far is the point (3, 4) from the origin (0, 0)? (a) 5 (b) 7 (c) 6 (d) 25
  30. 30.How far is the point (16, 12) from the origin (0, 0)? (a) 20 (b) 21 (c) 28 (d) 400
  31. 31.How far is the point (12, 9) from the origin (0, 0)? (a) 21 (b) 15 (c) 225 (d) 16
  32. 32.In which quadrant does the point (−5, 3) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  33. 33.What is the distance between the points (5, 1) and (10, 13)? (a) 14 (b) 17 (c) 169 (d) 13
  34. 34.What is the midpoint of the line joining (0, 14) and (6, 2)? (a) (6, 16) (b) (8, 3) (c) (3, 6) (d) (3, 8)
  35. 35.In which quadrant does the point (−3, 8) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  36. 36.What is the distance between the points (2, 15) and (8, 7)? (a) 11 (b) 10 (c) 100 (d) 14
  37. 37.What is the midpoint of the line joining (8, 0) and (10, 4)? (a) (1, 2) (b) (9, 2) (c) (2, 9) (d) (18, 4)
  38. 38.What is the distance between the points (7, 4) and (13, 12)? (a) 10 (b) 100 (c) 11 (d) 14
  39. 39.What is the midpoint of the line joining (6, 22) and (12, 10)? (a) (18, 32) (b) (3, 6) (c) (9, 16) (d) (16, 9)
  40. 40.In which quadrant does the point (−6, 6) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant

Answer key

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

Free maths olympiad lessons, practice and worksheets at talentjr.in/maths-olympiad