← Coordinates and distance lesson New set →

Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 948 · 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 (9, 4) and (13, 16)? (a) (10, 11) (b) (11, 10) (c) (2, 6) (d) (22, 20)
  2. 2.What is the midpoint of the line joining (1, 3) and (13, 9)? (a) (6, 7) (b) (7, 6) (c) (6, 3) (d) (14, 12)
  3. 3.What is the midpoint of the line joining (3, 6) and (9, 16)? (a) (6, 11) (b) (11, 6) (c) (12, 22) (d) (3, 5)
  4. 4.How far is the point (24, 7) from the origin (0, 0)? (a) 625 (b) 26 (c) 25 (d) 31
  5. 5.How far is the point (4, 3) from the origin (0, 0)? (a) 5 (b) 6 (c) 7 (d) 25
  6. 6.In which quadrant does the point (−3, 1) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  7. 7.What is the distance between the points (2, 22) and (14, 6)? (a) 400 (b) 28 (c) 20 (d) 21
  8. 8.How far is the point (12, 5) from the origin (0, 0)? (a) 169 (b) 13 (c) 17 (d) 14
  9. 9.In which quadrant does the point (−2, −8) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  10. 10.What is the distance between the points (9, 1) and (21, 6)? (a) 13 (b) 17 (c) 14 (d) 169
  11. 11.What is the midpoint of the line joining (6, 6) and (18, 0)? (a) (3, 12) (b) (12, 3) (c) (6, 3) (d) (24, 6)
  12. 12.What is the distance between the points (1, 5) and (7, 13)? (a) 14 (b) 100 (c) 11 (d) 10
  13. 13.What is the distance between the points (9, 4) and (13, 1)? (a) 7 (b) 6 (c) 5 (d) 25
  14. 14.How far is the point (8, 6) from the origin (0, 0)? (a) 14 (b) 10 (c) 11 (d) 100
  15. 15.What is the midpoint of the line joining (10, 9) and (16, 21)? (a) (26, 30) (b) (15, 13) (c) (13, 15) (d) (3, 6)
  16. 16.What is the midpoint of the line joining (1, 9) and (5, 13)? (a) (6, 22) (b) (3, 11) (c) (11, 3) (d) (2, 2)
  17. 17.What is the distance between the points (5, 21) and (13, 6)? (a) 17 (b) 289 (c) 18 (d) 23
  18. 18.What is the midpoint of the line joining (9, 1) and (15, 3)? (a) (24, 4) (b) (3, 1) (c) (2, 12) (d) (12, 2)
  19. 19.What is the midpoint of the line joining (5, 21) and (13, 9)? (a) (9, 15) (b) (15, 9) (c) (4, 6) (d) (18, 30)
  20. 20.What is the distance between the points (6, 5) and (9, 9)? (a) 7 (b) 6 (c) 5 (d) 25
  21. 21.What is the midpoint of the line joining (8, 0) and (16, 4)? (a) (4, 2) (b) (24, 4) (c) (2, 12) (d) (12, 2)
  22. 22.What is the midpoint of the line joining (2, 19) and (14, 9)? (a) (8, 14) (b) (6, 5) (c) (14, 8) (d) (16, 28)
  23. 23.What is the distance between the points (9, 0) and (24, 8)? (a) 23 (b) 289 (c) 17 (d) 18
  24. 24.What is the midpoint of the line joining (2, 7) and (14, 17)? (a) (8, 12) (b) (16, 24) (c) (6, 5) (d) (12, 8)
  25. 25.How far is the point (3, 4) from the origin (0, 0)? (a) 25 (b) 7 (c) 5 (d) 6
  26. 26.What is the midpoint of the line joining (10, 8) and (16, 2)? (a) (5, 13) (b) (3, 3) (c) (26, 10) (d) (13, 5)
  27. 27.What is the distance between the points (6, 12) and (14, 6)? (a) 14 (b) 11 (c) 100 (d) 10
  28. 28.What is the midpoint of the line joining (2, 12) and (14, 8)? (a) (10, 8) (b) (6, 2) (c) (16, 20) (d) (8, 10)
  29. 29.What is the distance between the points (4, 17) and (16, 1)? (a) 21 (b) 20 (c) 28 (d) 400
  30. 30.What is the midpoint of the line joining (9, 14) and (17, 4)? (a) (4, 5) (b) (13, 9) (c) (9, 13) (d) (26, 18)
  31. 31.What is the midpoint of the line joining (4, 5) and (6, 9)? (a) (7, 5) (b) (10, 14) (c) (5, 7) (d) (1, 2)
  32. 32.What is the distance between the points (2, 9) and (8, 1)? (a) 11 (b) 100 (c) 14 (d) 10
  33. 33.What is the distance between the points (9, 12) and (21, 7)? (a) 169 (b) 14 (c) 13 (d) 17
  34. 34.In which quadrant does the point (−2, 7) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  35. 35.What is the distance between the points (8, 5) and (12, 2)? (a) 7 (b) 5 (c) 6 (d) 25
  36. 36.In which quadrant does the point (6, 8) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  37. 37.What is the midpoint of the line joining (2, 20) and (10, 8)? (a) (4, 6) (b) (12, 28) (c) (14, 6) (d) (6, 14)
  38. 38.What is the distance between the points (6, 1) and (21, 9)? (a) 289 (b) 18 (c) 17 (d) 23
  39. 39.What is the distance between the points (7, 7) and (11, 10)? (a) 25 (b) 5 (c) 6 (d) 7
  40. 40.What is the distance between the points (5, 12) and (10, 0)? (a) 17 (b) 13 (c) 169 (d) 14

Answer key

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

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